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. (c) 2005 Elsevier Inc. All rights reserved.
Larsen, M., Schoof, R.j. (2006). A refined counter-example to the support conjecture for abelian varieties. JOURNAL OF NUMBER THEORY, 116(2), 396-398 [10.1016/j.jnt.2005.05.015].
A refined counter-example to the support conjecture for abelian varieties
SCHOOF, RENATUS JOHANNES
2006-01-01
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. (c) 2005 Elsevier Inc. All rights reserved.File in questo prodotto:
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