Vanishing of some Galois cohomology groups for elliptic curves
Abstract
Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the ptorsion points on E. We determine all cases when the Galois cohomology group H^1(G, E[p]) does not vanish, and investigate the analogous question for E[p^i] when i>1. We include an application to the verification of certain cases of the Birch and SwinnertonDyer conjecture, and another application to the GrunwaldWang problem for elliptic curves.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.02940
 Bibcode:
 2015arXiv150502940L
 Keywords:

 Mathematics  Number Theory