Non-trivial Geometric Homomorphisms of A and B
Abelian varies with isogenous reductions
If A and B are abelian varieties over a number field K such that there is 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 A --> B defined over the algebraic closure of K.