--- _id: '12312' abstract: - lang: eng 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 $\\ell$." 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." article_number: '18' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Davide full_name: Lombardo, Davide last_name: Lombardo - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: 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 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 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. 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. ista: Lombardo D, Verzobio M. 2024. On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. 30(2), 18. 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). date_created: 2023-01-16T11:45:53Z date_published: 2024-01-26T00:00:00Z date_updated: 2024-02-05T12:25:00Z day: '26' department: - _id: TiBr doi: 10.1007/s00029-023-00908-0 external_id: arxiv: - '2206.15240' intvolume: ' 30' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2206.15240 month: '01' oa: 1 oa_version: Preprint publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the local-global principle for isogenies of abelian surfaces type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2024' ... --- _id: '12311' abstract: - lang: eng 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. 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. article_number: '2203.02015' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Bartosz full_name: Naskręcki, Bartosz last_name: Naskręcki - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: 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' 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' 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.' 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.' ista: 'Naskręcki B, Verzobio M. 2024. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics., 2203.02015.' 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).' date_created: 2023-01-16T11:45:22Z date_published: 2024-02-26T00:00:00Z date_updated: 2024-03-13T11:55:21Z day: '26' ddc: - '510' department: - _id: TiBr doi: 10.1017/prm.2024.7 ec_funded: 1 external_id: arxiv: - '2203.02015' has_accepted_license: '1' keyword: - Elliptic curves - Néron models - division polynomials - height functions - discrete valuation rings language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1017/prm.2024.7 month: '02' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: 'Proceedings of the Royal Society of Edinburgh Section A: Mathematics' publication_identifier: eissn: - 1473-7124 issn: - 0308-2105 publication_status: epub_ahead publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Common valuations of division polynomials tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '13180' abstract: - lang: eng text: We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface article_processing_charge: No article_type: original author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Julian full_name: Lyczak, Julian id: 3572849A-F248-11E8-B48F-1D18A9856A87 last_name: Lyczak - first_name: Roman full_name: Sarapin, Roman last_name: Sarapin citation: 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 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 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. 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. 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. 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. date_created: 2023-07-02T22:00:43Z date_published: 2023-05-26T00:00:00Z date_updated: 2023-07-17T08:39:19Z day: '26' department: - _id: TiBr doi: 10.2140/involve.2023.16.331 external_id: arxiv: - '2203.06881' intvolume: ' 16' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2203.06881 month: '05' oa: 1 oa_version: Preprint page: 331-342 publication: Involve publication_identifier: eissn: - 1944-4184 issn: - 1944-4176 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Local solubility for a family of quadrics over a split quadric surface type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2023' ... --- _id: '9034' 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. 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. article_processing_charge: No article_type: original author: - first_name: Florian Alexander full_name: Wilsch, Florian Alexander id: 560601DA-8D36-11E9-A136-7AC1E5697425 last_name: Wilsch orcid: 0000-0001-7302-8256 citation: 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 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 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. 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. ista: Wilsch FA. 2023. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023(8), 6780–6808. 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. date_created: 2021-01-22T09:31:09Z date_published: 2023-04-01T00:00:00Z date_updated: 2023-08-01T12:23:55Z day: '01' department: - _id: TiBr doi: 10.1093/imrn/rnac048 external_id: arxiv: - '1901.08503' isi: - '000773116000001' intvolume: ' 2023' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1901.08503 month: '04' oa: 1 oa_version: Preprint page: 6780-6808 publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford Academic quality_controlled: '1' status: public title: Integral points of bounded height on a log Fano threefold type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 2023 year: '2023' ... --- _id: '12427' 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.' article_processing_charge: No article_type: original author: - first_name: Francesca full_name: Balestrieri, Francesca id: 3ACCD756-F248-11E8-B48F-1D18A9856A87 last_name: Balestrieri citation: 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 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. 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. 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. short: F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023) 907–914. date_created: 2023-01-29T23:00:58Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-08-01T13:03:32Z day: '01' department: - _id: TiBr doi: 10.1090/proc/15239 external_id: isi: - '000898440000001' intvolume: ' 151' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://hal.science/hal-03013498/ month: '01' oa: 1 oa_version: Preprint page: 907-914 publication: Proceedings of the American Mathematical Society publication_identifier: eissn: - 1088-6826 issn: - 0002-9939 publication_status: published publisher: American Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Some remarks on strong approximation and applications to homogeneous spaces of linear algebraic groups type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 151 year: '2023' ... --- _id: '13091' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Will full_name: Sawin, Will last_name: Sawin citation: 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 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 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. 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. 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. 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. date_created: 2023-05-28T22:01:02Z date_published: 2023-04-12T00:00:00Z date_updated: 2023-08-01T14:51:57Z day: '12' ddc: - '510' department: - _id: TiBr doi: 10.2140/ant.2023.17.719 external_id: arxiv: - '1810.06882' isi: - '000996014700004' file: - access_level: open_access checksum: 5d5d67b235905650e33cf7065d7583b4 content_type: application/pdf creator: dernst date_created: 2023-05-30T08:05:22Z date_updated: 2023-05-30T08:05:22Z file_id: '13101' file_name: 2023_AlgebraNumberTheory_Browning.pdf file_size: 1430719 relation: main_file success: 1 file_date_updated: 2023-05-30T08:05:22Z has_accepted_license: '1' intvolume: ' 17' isi: 1 issue: '3' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 719-748 project: - _id: 26A8D266-B435-11E9-9278-68D0E5697425 grant_number: EP-P026710-2 name: Between rational and integral points publication: Algebra and Number Theory publication_identifier: eissn: - 1944-7833 issn: - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Free rational curves on low degree hypersurfaces and the circle method tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 17 year: '2023' ... --- _id: '8682' abstract: - lang: eng 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. article_processing_charge: No article_type: original author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Pierre Le full_name: Boudec, Pierre Le last_name: Boudec - first_name: Will full_name: Sawin, Will last_name: Sawin citation: 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 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 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. 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. ista: Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203. 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. date_created: 2020-10-19T14:28:50Z date_published: 2023-05-01T00:00:00Z date_updated: 2023-10-17T12:47:43Z day: '01' department: - _id: TiBr doi: 10.4007/annals.2023.197.3.3 external_id: arxiv: - '2006.02356' isi: - '000966611000003' intvolume: ' 197' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2006.02356 month: '05' oa: 1 oa_version: Preprint page: 1115-1203 publication: Annals of Mathematics publication_identifier: issn: - 0003-486X publication_status: published publisher: Princeton University quality_controlled: '1' related_material: link: - description: News on IST Homepage relation: press_release url: https://ist.ac.at/en/news/when-is-necessary-sufficient/ status: public title: The Hasse principle for random Fano hypersurfaces type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 197 year: '2023' ... --- _id: '12916' abstract: - lang: eng 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" article_processing_charge: No article_type: original author: - first_name: Dante full_name: Bonolis, Dante id: 6A459894-5FDD-11E9-AF35-BB24E6697425 last_name: Bonolis - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: 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 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 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. 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. 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. 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. date_created: 2023-05-07T22:01:04Z date_published: 2023-02-16T00:00:00Z date_updated: 2023-10-18T06:54:30Z day: '16' department: - _id: TiBr doi: 10.2422/2036-2145.202010_018 external_id: arxiv: - '2007.14182' intvolume: ' 24' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2007.14182 month: '02' oa: 1 oa_version: Preprint page: 173-204 publication: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze publication_identifier: eissn: - 2036-2145 issn: - 0391-173X publication_status: published publisher: Scuola Normale Superiore - Edizioni della Normale quality_controlled: '1' scopus_import: '1' status: public title: Uniform bounds for rational points on hyperelliptic fibrations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '12313' 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. 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." article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 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 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 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. 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. ista: Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic divisibility  sequences. Pacific Journal of Mathematics. 325(2), 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. short: M. Verzobio, Pacific Journal of Mathematics 325 (2023) 331–351. date_created: 2023-01-16T11:46:19Z date_published: 2023-11-03T00:00:00Z date_updated: 2023-12-13T11:18:14Z day: '03' ddc: - '510' department: - _id: TiBr doi: 10.2140/pjm.2023.325.331 ec_funded: 1 external_id: arxiv: - '2001.02987' isi: - '001104766900001' file: - access_level: open_access checksum: b6218d16a72742d8bb38d6fc3c9bb8c6 content_type: application/pdf creator: dernst date_created: 2023-11-13T09:50:41Z date_updated: 2023-11-13T09:50:41Z file_id: '14525' file_name: 2023_PacificJourMaths_Verzobio.pdf file_size: 389897 relation: main_file success: 1 file_date_updated: 2023-11-13T09:50:41Z has_accepted_license: '1' intvolume: ' 325' isi: 1 issue: '2' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 331-351 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Pacific Journal of Mathematics publication_identifier: eissn: - 0030-8730 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Some effectivity results for primitive divisors of elliptic divisibility sequences tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 325 year: '2023' ... --- _id: '13973' 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. 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." article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Julian full_name: Lyczak, Julian id: 3572849A-F248-11E8-B48F-1D18A9856A87 last_name: Lyczak citation: 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 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 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. 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. 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. 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. date_created: 2023-08-06T22:01:12Z date_published: 2023-05-12T00:00:00Z date_updated: 2023-12-13T12:03:04Z day: '12' ddc: - '510' department: - _id: TiBr doi: 10.5802/aif.3529 ec_funded: 1 external_id: arxiv: - '2005.14013' isi: - '001000279500001' file: - access_level: open_access checksum: daf53fc614c894422e4c0fb3d2a2ae3e content_type: application/pdf creator: dernst date_created: 2023-08-07T07:19:42Z date_updated: 2023-08-07T07:19:42Z file_id: '13977' file_name: 2023_AnnalesFourier_Lyczak.pdf file_size: 1529821 relation: main_file success: 1 file_date_updated: 2023-08-07T07:19:42Z has_accepted_license: '1' intvolume: ' 73' isi: 1 issue: '2' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '05' oa: 1 oa_version: Published Version page: 447-478 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Annales de l'Institut Fourier publication_identifier: issn: - 0373-0956 publication_status: published publisher: Association des Annales de l'Institut Fourier quality_controlled: '1' scopus_import: '1' status: public title: Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3 surfaces tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 73 year: '2023' ...