Vanishing of some Galois cohomology groups for elliptic curvesTools Lawson, Tyler and Wuthrich, Christian (2016) Vanishing of some Galois cohomology groups for elliptic curves. In: Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer proceedings in mathematics & statistics (188). Springer, pp. 373399. ISBN 9783319450322
AbstractLet 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 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 SwinnertonDyer conjecture, and another application to the GrunwaldWang problem for elliptic curves.
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