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

Michael Larsen·René Schoof
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Abstract

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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Michael Larsen, René Schoof. 2005-02-13. A refined counter-example to the support conjecture for abelian varieties. https://arxiv.org/abs/math/0502261

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