---
res:
bibo_abstract:
- "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
$\\ell$.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Davide
foaf_name: Lombardo, Davide
foaf_surname: Lombardo
- foaf_Person:
foaf_givenName: Matteo
foaf_name: Verzobio, Matteo
foaf_surname: Verzobio
foaf_workInfoHomepage: http://www.librecat.org/personId=7aa8f170-131e-11ed-88e1-a9efd01027cb
orcid: 0000-0002-0854-0306
bibo_doi: 10.1007/s00029-023-00908-0
bibo_issue: '2'
bibo_volume: 30
dct_date: 2024^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1022-1824
- http://id.crossref.org/issn/1420-9020
dct_language: eng
dct_publisher: Springer Nature@
dct_title: On the local-global principle for isogenies of abelian surfaces@
...