The constant of the support problem for abelian varieties

2010/08/22 by Jeroen Demeyer, Antonella Perucca, Demeyer, Jeroen +1
Computer Science · Mathematics · #11G10 #14K15 (Primary) #14L10 (Secondary) #16H10 #16S50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.1008.3719

openalex publication_date 2010/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The support problem for abelian varieties
• A refined counter-example to the support conjecture for abelian\n varieties
• The multilinear support problem for products of abelian varieties and tori
• Reduction of homomorphisms mod p and algebraicity
• Endomorphism fields of abelian varieties