The constant of the support problem for abelian varieties

Abstract

Let A be an abelian variety defined over a number field K and let P and Q be points in A(K) satisfying the following condition: for all but finitely many primes p of K, the order of (Q mod p) divides the order of (P mod p). Larsen proved that there exists a positive integer c such that cQ is in the End_K(A)-module generated by P. We study the minimal value of c and construct some refined counterexamples.

Minor changes

References in corpus (2)

• Prescribing valuations of the order of a point in the reductions of abelian varieties and tori
• Two variants of the support problem for products of abelian varieties and tori