Michael Larsen
Published 2002-11-06, updated 2003-02-28Version 3
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 $\phi$ of $A$ and a positive integer $k$ such that $kQ = \phi(P)$.
Comments: 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
On reduction maps and support problem in K-theory and abelian varieties
A refined counter-example to the support conjecture for abelian varieties
Kummer theory of abelian varieties and reductions of Mordell-Weil groups
![QR code for arXiv:math/0211118 [math.NT]](http://oss.arxitics.com/images/favicon.svg)