---
_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'
...