The support problem for abelian varieties

2002/11/06 by Michael Larsen, Larsen, Michael · 1 citation
Agricultural and Biological Sciences · Computer Science · Mathematics · #11G10 #11R34 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Plant responses to water stress #Polynomial and algebraic computation #math.NT #msc:11G10 #msc:11R34

paper · pdf · doi:10.48550/arxiv.math/0211118

7 pages, plain TeX. The statements of the main theorem and main corollary are slightly weakened to coincide with what is actually proved in the paper. There are a few other minor changes. To appear in the Journal of Number Theory

openalex publication_date 2002/11/06 · arxiv created 2003/02/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be an abelian variety over a number field K. If P and Q are K-rational points of A such that the order of the reduction of Q divides that of P for all but finitely many primes of the ring of integers of K, then there exists a K-endomorphism ϕ of A and a positive integer k such that kQ = ϕ(P).

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