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Vanishing of some Galois cohomology groups for elliptic curves

Lawson, Tyler; Wuthrich, Christian

Authors

Tyler Lawson



Contributors

David Loeffler
Editor

Sarah Livia Zerbes
Editor

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.

Citation

Lawson, T., & Wuthrich, C. (2016). Vanishing of some Galois cohomology groups for elliptic curves. In D. Loeffler, & S. L. Zerbes (Eds.), Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer

Acceptance Date Jan 1, 2017
Publication Date Jan 1, 2016
Deposit Date Feb 21, 2017
Publicly Available Date Mar 29, 2024
Peer Reviewed Peer Reviewed
Issue 188
Series Title Springer proceedings in mathematics & statistics
Book Title Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015
ISBN 978-3-319-45032-2
Public URL https://nottingham-repository.worktribe.com/output/980152
Related Public URLs http://www.springer.com/gb/book/9783319450315
Additional Information DOI of book: 10.1007/978-3-319-45032-2