Vanishing of some Galois cohomology groups for elliptic curves

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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. 373-399. ISBN 978-3-319-45032-2

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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.

Item Type:

Book Section

RIS ID:

https://nottingham-repository.worktribe.com/output/980152

Additional Information:

DOI of book: 10.1007/978-3-319-45032-2

Schools/Departments:

University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences

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