[{"article_number":"18","author":[{"last_name":"Lombardo","first_name":"Davide","full_name":"Lombardo, Davide"},{"full_name":"Verzobio, Matteo","first_name":"Matteo","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306"}],"volume":30,"date_updated":"2024-02-05T12:25:00Z","date_created":"2023-01-16T11:45:53Z","acknowledgement":"It is a pleasure to thank Samuele Anni for his interest in this project and for several discussions on the topic of this paper, which led in particular to Remark 6.30 and to a better understanding of the difficulties with [6]. We also thank John Cullinan for correspondence about [6] and Barinder Banwait for his many insightful comments on the first version of this paper. Finally, we thank the referee for their thorough reading of the manuscript.\r\nOpen access funding provided by Università di Pisa within the CRUI-CARE Agreement. The authors have been partially supported by MIUR (Italy) through PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic\" and PRIN 2022 “Semiabelian varieties, Galois representations and related Diophantine problems\", and by the University of Pisa through PRA 2018-19 and 2022 “Spazi di moduli, rappresentazioni e strutture combinatorie\". The first author is a member of the INdAM group GNSAGA.","year":"2024","publisher":"Springer Nature","department":[{"_id":"TiBr"}],"publication_status":"epub_ahead","publication_identifier":{"issn":["1022-1824"],"eissn":["1420-9020"]},"month":"01","doi":"10.1007/s00029-023-00908-0","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2206.15240","open_access":"1"}],"oa":1,"external_id":{"arxiv":["2206.15240"]},"quality_controlled":"1","issue":"2","abstract":[{"text":"Let $\\ell$ be a prime number. We classify the subgroups $G$ of $\\operatorname{Sp}_4(\\mathbb{F}_\\ell)$ and $\\operatorname{GSp}_4(\\mathbb{F}_\\ell)$ that act irreducibly on $\\mathbb{F}_\\ell^4$, but such that every element of $G$ fixes an $\\mathbb{F}_\\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\\ell$ for which some abelian surface\r\n$A/\\mathbb{Q}$ fails the local-global principle for isogenies of degree $\\ell$.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12312","intvolume":" 30","status":"public","title":"On the local-global principle for isogenies of abelian surfaces","article_processing_charge":"Yes (via OA deal)","day":"26","scopus_import":"1","date_published":"2024-01-26T00:00:00Z","citation":{"mla":"Lombardo, Davide, and Matteo Verzobio. “On the Local-Global Principle for Isogenies of Abelian Surfaces.” Selecta Mathematica, vol. 30, no. 2, 18, Springer Nature, 2024, doi:10.1007/s00029-023-00908-0.","short":"D. Lombardo, M. Verzobio, Selecta Mathematica 30 (2024).","chicago":"Lombardo, Davide, and Matteo Verzobio. “On the Local-Global Principle for Isogenies of Abelian Surfaces.” Selecta Mathematica. Springer Nature, 2024. https://doi.org/10.1007/s00029-023-00908-0.","ama":"Lombardo D, Verzobio M. On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. 2024;30(2). doi:10.1007/s00029-023-00908-0","ista":"Lombardo D, Verzobio M. 2024. On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. 30(2), 18.","apa":"Lombardo, D., & Verzobio, M. (2024). On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-023-00908-0","ieee":"D. Lombardo and M. Verzobio, “On the local-global principle for isogenies of abelian surfaces,” Selecta Mathematica, vol. 30, no. 2. Springer Nature, 2024."},"publication":"Selecta Mathematica","article_type":"original"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12311","title":"Common valuations of division polynomials","status":"public","ddc":["510"],"oa_version":"Published Version","type":"journal_article","abstract":[{"text":"In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.","lang":"eng"}],"citation":{"ista":"Naskręcki B, Verzobio M. 2024. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics., 2203.02015.","apa":"Naskręcki, B., & Verzobio, M. (2024). Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press. https://doi.org/10.1017/prm.2024.7","ieee":"B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press, 2024.","ama":"Naskręcki B, Verzobio M. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2024. doi:10.1017/prm.2024.7","chicago":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press, 2024. https://doi.org/10.1017/prm.2024.7.","mla":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2203.02015, Cambridge University Press, 2024, doi:10.1017/prm.2024.7.","short":"B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2024)."},"publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","article_type":"original","date_published":"2024-02-26T00:00:00Z","scopus_import":"1","keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"26","year":"2024","acknowledgement":"Silverman, and Paul Voutier for the comments on the earlier version of this paper. The first author acknowledges the support by Dioscuri programme initiated by the Max Planck Society, jointly managed with the National Science Centre (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research. The second author has been supported by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in arithmetic’ and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","department":[{"_id":"TiBr"}],"publisher":"Cambridge University Press","publication_status":"epub_ahead","author":[{"first_name":"Bartosz","last_name":"Naskręcki","full_name":"Naskręcki, Bartosz"},{"first_name":"Matteo","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo"}],"date_updated":"2024-03-13T11:55:21Z","date_created":"2023-01-16T11:45:22Z","article_number":"2203.02015","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2203.02015"]},"main_file_link":[{"url":"https://doi.org/10.1017/prm.2024.7","open_access":"1"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"quality_controlled":"1","doi":"10.1017/prm.2024.7","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1473-7124"],"issn":["0308-2105"]},"month":"02"},{"date_published":"2023-05-26T00:00:00Z","page":"331-342","article_type":"original","citation":{"mla":"Browning, Timothy D., et al. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” Involve, vol. 16, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–42, doi:10.2140/involve.2023.16.331.","short":"T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342.","chicago":"Browning, Timothy D, Julian Lyczak, and Roman Sarapin. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” Involve. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/involve.2023.16.331.","ama":"Browning TD, Lyczak J, Sarapin R. Local solubility for a family of quadrics over a split quadric surface. Involve. 2023;16(2):331-342. doi:10.2140/involve.2023.16.331","ista":"Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics over a split quadric surface. Involve. 16(2), 331–342.","apa":"Browning, T. D., Lyczak, J., & Sarapin, R. (2023). Local solubility for a family of quadrics over a split quadric surface. Involve. Mathematical Sciences Publishers. https://doi.org/10.2140/involve.2023.16.331","ieee":"T. D. Browning, J. Lyczak, and R. Sarapin, “Local solubility for a family of quadrics over a split quadric surface,” Involve, vol. 16, no. 2. Mathematical Sciences Publishers, pp. 331–342, 2023."},"publication":"Involve","article_processing_charge":"No","day":"26","scopus_import":"1","oa_version":"Preprint","intvolume":" 16","title":"Local solubility for a family of quadrics over a split quadric surface","status":"public","_id":"13180","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","abstract":[{"text":"We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.2140/involve.2023.16.331","quality_controlled":"1","oa":1,"external_id":{"arxiv":["2203.06881"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2203.06881"}],"publication_identifier":{"eissn":["1944-4184"],"issn":["1944-4176"]},"month":"05","volume":16,"date_updated":"2023-07-17T08:39:19Z","date_created":"2023-07-02T22:00:43Z","author":[{"first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Lyczak, Julian","first_name":"Julian","last_name":"Lyczak","id":"3572849A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Sarapin","first_name":"Roman","full_name":"Sarapin, Roman"}],"department":[{"_id":"TiBr"}],"publisher":"Mathematical Sciences Publishers","publication_status":"published","year":"2023"},{"author":[{"id":"560601DA-8D36-11E9-A136-7AC1E5697425","orcid":"0000-0001-7302-8256","first_name":"Florian Alexander","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander"}],"volume":2023,"date_created":"2021-01-22T09:31:09Z","date_updated":"2023-08-01T12:23:55Z","acknowledgement":"This work was supported by the German Academic Exchange Service. Parts of this article were prepared at the Institut de Mathémathiques de Jussieu—Paris Rive Gauche. I wish to thank Antoine Chambert-Loir for his remarks and the institute for its hospitality, as well as the anonymous referee for several useful remarks and suggestions for improvements.","year":"2023","publisher":"Oxford Academic","department":[{"_id":"TiBr"}],"publication_status":"published","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"month":"04","doi":"10.1093/imrn/rnac048","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1901.08503"],"isi":["000773116000001"]},"main_file_link":[{"url":"https://arxiv.org/abs/1901.08503","open_access":"1"}],"quality_controlled":"1","isi":1,"issue":"8","abstract":[{"lang":"eng","text":"We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of P3 outside certain planes using universal torsors."}],"type":"journal_article","oa_version":"Preprint","_id":"9034","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 2023","title":"Integral points of bounded height on a log Fano threefold","status":"public","article_processing_charge":"No","day":"01","date_published":"2023-04-01T00:00:00Z","citation":{"mla":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” International Mathematics Research Notices, vol. 2023, no. 8, Oxford Academic, 2023, pp. 6780–808, doi:10.1093/imrn/rnac048.","short":"F.A. Wilsch, International Mathematics Research Notices 2023 (2023) 6780–6808.","chicago":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” International Mathematics Research Notices. Oxford Academic, 2023. https://doi.org/10.1093/imrn/rnac048.","ama":"Wilsch FA. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023;2023(8):6780-6808. doi:10.1093/imrn/rnac048","ista":"Wilsch FA. 2023. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023(8), 6780–6808.","ieee":"F. A. Wilsch, “Integral points of bounded height on a log Fano threefold,” International Mathematics Research Notices, vol. 2023, no. 8. Oxford Academic, pp. 6780–6808, 2023.","apa":"Wilsch, F. A. (2023). Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. Oxford Academic. https://doi.org/10.1093/imrn/rnac048"},"publication":"International Mathematics Research Notices","page":"6780-6808","article_type":"original"},{"publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"month":"01","doi":"10.1090/proc/15239","language":[{"iso":"eng"}],"external_id":{"isi":["000898440000001"]},"main_file_link":[{"open_access":"1","url":"https://hal.science/hal-03013498/"}],"oa":1,"quality_controlled":"1","isi":1,"author":[{"id":"3ACCD756-F248-11E8-B48F-1D18A9856A87","last_name":"Balestrieri","first_name":"Francesca","full_name":"Balestrieri, Francesca"}],"volume":151,"date_created":"2023-01-29T23:00:58Z","date_updated":"2023-08-01T13:03:32Z","year":"2023","publisher":"American Mathematical Society","department":[{"_id":"TiBr"}],"publication_status":"published","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2023-01-01T00:00:00Z","citation":{"short":"F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023) 907–914.","mla":"Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American Mathematical Society, vol. 151, no. 3, American Mathematical Society, 2023, pp. 907–14, doi:10.1090/proc/15239.","chicago":"Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/15239.","ama":"Balestrieri F. Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. 2023;151(3):907-914. doi:10.1090/proc/15239","apa":"Balestrieri, F. (2023). Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15239","ieee":"F. Balestrieri, “Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups,” Proceedings of the American Mathematical Society, vol. 151, no. 3. American Mathematical Society, pp. 907–914, 2023.","ista":"Balestrieri F. 2023. Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups. Proceedings of the American Mathematical Society. 151(3), 907–914."},"publication":"Proceedings of the American Mathematical Society","page":"907-914","article_type":"original","issue":"3","abstract":[{"lang":"eng","text":"Let k be a number field and X a smooth, geometrically integral quasi-projective variety over k. For any linear algebraic group G over k and any G-torsor g : Z → X, we observe that if the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for all twists of Z by elements in H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation off a finite set of places S for X. As an application, we show that any homogeneous space of the form G/H with G a connected linear algebraic group over k satisfies strong approximation off the infinite places with étale-Brauer obstruction, under some compactness assumptions when k is totally real. We also prove more refined strong approximation results for homogeneous spaces of the form G/H with G semisimple simply connected and H finite, using the theory of torsors and descent."}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12427","intvolume":" 151","title":"Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups","status":"public"},{"project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"}],"isi":1,"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000996014700004"],"arxiv":["1810.06882"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.2140/ant.2023.17.719","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"month":"04","publisher":"Mathematical Sciences Publishers","department":[{"_id":"TiBr"}],"publication_status":"published","year":"2023","acknowledgement":"The authors are grateful to Paul Nelson, Per Salberger and Jason Starr for useful comments. While working on this paper the first author was supported by EPRSC grant EP/P026710/1. The research was partially conducted during the period the second author served as a Clay Research Fellow, and partially conducted during the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.","volume":17,"date_created":"2023-05-28T22:01:02Z","date_updated":"2023-08-01T14:51:57Z","author":[{"last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"}],"file_date_updated":"2023-05-30T08:05:22Z","page":"719-748","article_type":"original","citation":{"chicago":"Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/ant.2023.17.719.","mla":"Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory, vol. 17, no. 3, Mathematical Sciences Publishers, 2023, pp. 719–48, doi:10.2140/ant.2023.17.719.","short":"T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748.","ista":"Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 17(3), 719–748.","apa":"Browning, T. D., & Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2023.17.719","ieee":"T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces and the circle method,” Algebra and Number Theory, vol. 17, no. 3. Mathematical Sciences Publishers, pp. 719–748, 2023.","ama":"Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 2023;17(3):719-748. doi:10.2140/ant.2023.17.719"},"publication":"Algebra and Number Theory","date_published":"2023-04-12T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"No","day":"12","intvolume":" 17","status":"public","title":"Free rational curves on low degree hypersurfaces and the circle method","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"13091","oa_version":"Published Version","file":[{"file_id":"13101","relation":"main_file","date_created":"2023-05-30T08:05:22Z","date_updated":"2023-05-30T08:05:22Z","success":1,"checksum":"5d5d67b235905650e33cf7065d7583b4","file_name":"2023_AlgebraNumberTheory_Browning.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":1430719}],"type":"journal_article","issue":"3","abstract":[{"text":"We use a function field version of the Hardy–Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the dimension of the singular locus of the moduli space of rational curves on such hypersurfaces and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin conjecture in terms of slopes with respect to the tangent bundle.","lang":"eng"}]},{"external_id":{"arxiv":["2006.02356"],"isi":["000966611000003"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.02356"}],"oa":1,"quality_controlled":"1","isi":1,"doi":"10.4007/annals.2023.197.3.3","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0003-486X"]},"month":"05","year":"2023","publisher":"Princeton University","department":[{"_id":"TiBr"}],"publication_status":"published","related_material":{"link":[{"url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/","relation":"press_release","description":"News on IST Homepage"}]},"author":[{"full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"full_name":"Boudec, Pierre Le","first_name":"Pierre Le","last_name":"Boudec"},{"full_name":"Sawin, Will","last_name":"Sawin","first_name":"Will"}],"volume":197,"date_created":"2020-10-19T14:28:50Z","date_updated":"2023-10-17T12:47:43Z","citation":{"ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.","ieee":"T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” Annals of Mathematics, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023.","apa":"Browning, T. D., Boudec, P. L., & Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. Princeton University. https://doi.org/10.4007/annals.2023.197.3.3","ama":"Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 2023;197(3):1115-1203. doi:10.4007/annals.2023.197.3.3","chicago":"Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” Annals of Mathematics. Princeton University, 2023. https://doi.org/10.4007/annals.2023.197.3.3.","mla":"Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” Annals of Mathematics, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:10.4007/annals.2023.197.3.3.","short":"T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203."},"publication":"Annals of Mathematics","page":"1115-1203","article_type":"original","date_published":"2023-05-01T00:00:00Z","article_processing_charge":"No","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8682","intvolume":" 197","title":"The Hasse principle for random Fano hypersurfaces","status":"public","oa_version":"Preprint","type":"journal_article","issue":"3","abstract":[{"text":"It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.","lang":"eng"}]},{"publication_identifier":{"eissn":["2036-2145"],"issn":["0391-173X"]},"month":"02","quality_controlled":"1","oa":1,"external_id":{"arxiv":["2007.14182"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2007.14182"}],"language":[{"iso":"eng"}],"doi":"10.2422/2036-2145.202010_018","publisher":"Scuola Normale Superiore - Edizioni della Normale","department":[{"_id":"TiBr"}],"publication_status":"published","year":"2023","volume":24,"date_updated":"2023-10-18T06:54:30Z","date_created":"2023-05-07T22:01:04Z","author":[{"full_name":"Bonolis, Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","last_name":"Bonolis","first_name":"Dante"},{"full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","article_processing_charge":"No","day":"16","page":"173-204","article_type":"original","citation":{"mla":"Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della Normale, 2023, pp. 173–204, doi:10.2422/2036-2145.202010_018.","short":"D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204.","chicago":"Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2023. https://doi.org/10.2422/2036-2145.202010_018.","ama":"Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2023;24(1):173-204. doi:10.2422/2036-2145.202010_018","ista":"Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 24(1), 173–204.","apa":"Bonolis, D., & Browning, T. D. (2023). Uniform bounds for rational points on hyperelliptic fibrations. Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202010_018","ieee":"D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic fibrations,” Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204, 2023."},"publication":"Annali della Scuola Normale Superiore di Pisa - Classe di Scienze","date_published":"2023-02-16T00:00:00Z","type":"journal_article","issue":"1","abstract":[{"text":"We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface.\r\n","lang":"eng"}],"intvolume":" 24","title":"Uniform bounds for rational points on hyperelliptic fibrations","status":"public","_id":"12916","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint"},{"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"isi":1,"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["001104766900001"],"arxiv":["2001.02987"]},"language":[{"iso":"eng"}],"doi":"10.2140/pjm.2023.325.331","publication_identifier":{"eissn":["0030-8730"]},"month":"11","department":[{"_id":"TiBr"}],"publisher":"Mathematical Sciences Publishers","publication_status":"published","acknowledgement":"This paper is part of the author’s PhD thesis at Università of Pisa. Moreover, this\r\nproject has received funding from the European Union’s Horizon 2020 research\r\nand innovation programme under the Marie Skłodowska-Curie Grant Agreement\r\nNo. 101034413. I thank the referee for many helpful comments.","year":"2023","volume":325,"date_created":"2023-01-16T11:46:19Z","date_updated":"2023-12-13T11:18:14Z","author":[{"last_name":"Verzobio","first_name":"Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo"}],"ec_funded":1,"file_date_updated":"2023-11-13T09:50:41Z","page":"331-351","article_type":"original","citation":{"ama":"Verzobio M. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 2023;325(2):331-351. doi:10.2140/pjm.2023.325.331","ieee":"M. Verzobio, “Some effectivity results for primitive divisors of elliptic divisibility sequences,” Pacific Journal of Mathematics, vol. 325, no. 2. Mathematical Sciences Publishers, pp. 331–351, 2023.","apa":"Verzobio, M. (2023). Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2023.325.331","ista":"Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 325(2), 331–351.","short":"M. Verzobio, Pacific Journal of Mathematics 325 (2023) 331–351.","mla":"Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility Sequences.” Pacific Journal of Mathematics, vol. 325, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–51, doi:10.2140/pjm.2023.325.331.","chicago":"Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility Sequences.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pjm.2023.325.331."},"publication":"Pacific Journal of Mathematics","date_published":"2023-11-03T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","day":"03","intvolume":" 325","status":"public","title":"Some effectivity results for primitive divisors of elliptic divisibility sequences","ddc":["510"],"_id":"12313","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_name":"2023_PacificJourMaths_Verzobio.pdf","access_level":"open_access","content_type":"application/pdf","file_size":389897,"creator":"dernst","relation":"main_file","file_id":"14525","date_updated":"2023-11-13T09:50:41Z","date_created":"2023-11-13T09:50:41Z","checksum":"b6218d16a72742d8bb38d6fc3c9bb8c6","success":1}],"oa_version":"Published Version","type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"Let P be a nontorsion point on an elliptic curve defined over a number field K and consider the sequence {Bn}n∈N of the denominators of x(nP). We prove that every term of the sequence of the Bn has a primitive divisor for n greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve."}]},{"department":[{"_id":"TiBr"}],"publisher":"Association des Annales de l'Institut Fourier","publication_status":"published","acknowledgement":"This paper was completed as part of a project which received funding from the\r\nEuropean Union’s Horizon 2020 research and innovation programme under the Marie\r\nSkłodowska-Curie grant agreement No. 754411.","year":"2023","volume":73,"date_updated":"2023-12-13T12:03:04Z","date_created":"2023-08-06T22:01:12Z","author":[{"id":"3572849A-F248-11E8-B48F-1D18A9856A87","first_name":"Julian","last_name":"Lyczak","full_name":"Lyczak, Julian"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","ec_funded":1,"file_date_updated":"2023-08-07T07:19:42Z","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"quality_controlled":"1","isi":1,"tmp":{"short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"external_id":{"isi":["001000279500001"],"arxiv":["2005.14013"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.5802/aif.3529","publication_identifier":{"issn":["0373-0956"]},"month":"05","intvolume":" 73","ddc":["510"],"title":"Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13973","oa_version":"Published Version","file":[{"checksum":"daf53fc614c894422e4c0fb3d2a2ae3e","success":1,"date_created":"2023-08-07T07:19:42Z","date_updated":"2023-08-07T07:19:42Z","relation":"main_file","file_id":"13977","content_type":"application/pdf","file_size":1529821,"creator":"dernst","access_level":"open_access","file_name":"2023_AnnalesFourier_Lyczak.pdf"}],"type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"We construct families of log K3 surfaces and study the arithmetic of their members. We use this to produce explicit surfaces with an order 5 Brauer–Manin obstruction to the integral Hasse principle."}],"page":"447-478","article_type":"original","citation":{"ista":"Lyczak J. 2023. Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces. Annales de l’Institut Fourier. 73(2), 447–478.","apa":"Lyczak, J. (2023). Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces. Annales de l’Institut Fourier. Association des Annales de l’Institut Fourier. https://doi.org/10.5802/aif.3529","ieee":"J. Lyczak, “Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces,” Annales de l’Institut Fourier, vol. 73, no. 2. Association des Annales de l’Institut Fourier, pp. 447–478, 2023.","ama":"Lyczak J. Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces. Annales de l’Institut Fourier. 2023;73(2):447-478. doi:10.5802/aif.3529","chicago":"Lyczak, Julian. “Order 5 Brauer–Manin Obstructions to the Integral Hasse Principle on Log K3 Surfaces.” Annales de l’Institut Fourier. Association des Annales de l’Institut Fourier, 2023. https://doi.org/10.5802/aif.3529.","mla":"Lyczak, Julian. “Order 5 Brauer–Manin Obstructions to the Integral Hasse Principle on Log K3 Surfaces.” Annales de l’Institut Fourier, vol. 73, no. 2, Association des Annales de l’Institut Fourier, 2023, pp. 447–78, doi:10.5802/aif.3529.","short":"J. Lyczak, Annales de l’Institut Fourier 73 (2023) 447–478."},"publication":"Annales de l'Institut Fourier","date_published":"2023-05-12T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","day":"12"}]