Abelian varieties with isogenous reductions
Number Theory
2020-10-08 v3
Abstract
If A and B are abelian varieties over a number field K such that there are non-trivial geometric homomorphisms of abelian varieties between reductions of A and B at most primes of K, then there exists a non-trivial (geometric) homomorphism from A to B defined over an algebraic closure of K.
Cite
@article{arxiv.2009.01435,
title = {Abelian varieties with isogenous reductions},
author = {Chandrashekhar B. Khare and Michael Larsen},
journal= {arXiv preprint arXiv:2009.01435},
year = {2020}
}
Comments
Final version, with French abstract; to appear in Comptes Rendus - S\'erie Math\'ematique