Counterexamples to the local-global divisibility over elliptic curves
نویسنده
چکیده
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 pn does not hold over E(k).
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