The support problem for abelian varieties

Michael Larsen

The support problem for abelian varieties

Number Theory 2007-05-23 v3

Authors: Michael Larsen

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 $\phi$ of $A$ and a positive integer $k$ such that $kQ = \phi(P)$ .

Keywords

abelian varieties finite fields abelian groups

Cite

@article{arxiv.math/0211118,
  title  = {The support problem for abelian varieties},
  author = {Michael Larsen},
  journal= {arXiv preprint arXiv:math/0211118},
  year   = {2007}
}

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

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