Vanishing of some Galois cohomology groups for elliptic curves

2015/05/12 by Tyler Lawson, Lawson, Tyler, Christian Wuthrich +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1505.02940

arxiv created 2015/09/23 · arxiv updated 2015/09/24

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 p-torsion points on E. We determine all cases when the Galois cohomology group H¹(G, E[p]) does not vanish, and investigate the analogous question for E[pⁱ] when i>1. We include an application to the verification of certain cases of the Birch and Swinnerton-Dyer conjecture, and another application to the Grunwald-Wang problem for elliptic curves.

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