English

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.

Keywords

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

R2 v1 2026-06-23T18:17:02.990Z