--- _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' ...