Counterexamples to the local-global divisibility over elliptic curves
Let p≥5 be a prime number. We find all the possible subgroups G of GL2(Z/pZ) such that there exists a number field k and an elliptic curve E defined over k such that the Gal(k(E[p])/k)-module E[p] is isomorphic to the G-module (Z/pZ)^2 and there exists n∈N such that the local-global divisibility by p^n does not hold over E(k).
Autores: Gabriele Ranieri,
URL de la publicación: https://arxiv.org/pdf/1705.01880.pdf