# Vanishing of Some Galois Cohomology Groups for Elliptic Curves

@inproceedings{Lawson2015VanishingOS, title={Vanishing of Some Galois Cohomology Groups for Elliptic Curves}, author={T. Lawson and C. Wuthrich}, year={2015} }

Let \(E/\mathbb {Q}\) be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of \(\mathbb {Q}\) obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group \(H^1\bigl ( G, E[p]\bigr )\) 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 Swinnerton-Dyer conjecture, and another… CONTINUE READING

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