A refined counter-example to the support conjecture for abelian varieties

Details A refined counter-example to the support conjecture for abelian varieties A refined counter-example to the support conjecture for abelian varieties

2005-02-13

arxiv.org/abs/math/0502261v1

Mathematics

Number Theory

3 pages

Scientific paper

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.

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