The support problem for abelian varieties

Details The support problem for abelian varieties The support problem for abelian varieties

2002-11-06

arxiv.org/abs/math/0211118v3

Mathematics

Number Theory

7 pages, plain TeX. The statements of the main theorem and main corollary are slightly weakened to coincide with what is actua

Scientific paper

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 $kQ = \phi(P)$.

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