A refined counter-example to the support conjecture for abelian varieties
数论
2016-09-07 v1
摘要
If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mod p) for almost all primes p of K, then Q is obtained from P by applying an endomorphism of A. This is now known to be untrue. In this note we prove that it is not even true modulo the torsion of A.
引用
@article{arxiv.math/0502261,
title = {A refined counter-example to the support conjecture for abelian varieties},
author = {Michael Larsen and René Schoof},
journal= {arXiv preprint arXiv:math/0502261},
year = {2016}
}
备注
3 pages