Counterexamples to the local–global divisibility over elliptic curves

Resumen

Let p≥5 be a prime number. We find all the possible subgroups G of GL2( Z/pZ ) such that there exist 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

Journal: Annali di Matematica Pura ed Applicata

Journal Volume: 197

Journal Issue: 4

Journal Page: 1215-1225

Tipo de publicación: ISI

Fecha de publicación: 2018

Topics: Elliptic curves, local-global, Galois cohomology

DOI: https://doi.org/10.1007/s10231-017-0721-9

URL de la publicación: https://link.springer.com/article/10.1007%2Fs10231-017-0721-9#citeas