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

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 image divides the order of image for almost all primes image 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.