@inproceedings{6cba7d5ce80e4a4ebe28ef7003be500c,

title = "Vanishing of some galois cohomology groups for elliptic curves",

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.",

keywords = "Birch and Swinnerton-Dyer conjecture, Elliptic curves, Galois cohomology, Grunwald-Wang problem",

author = "Tyler Lawson and Christian Wuthrich",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016 Copyright: Copyright 2017 Elsevier B.V., All rights reserved.; Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 ; Conference date: 25-03-2015 Through 27-03-2015",

year = "2016",

doi = "10.1007/978-3-319-45032-2_11",

language = "English (US)",

isbn = "9783319450315",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "373--399",

editor = "David Loeffler and Zerbes, {Sarah Livia}",

booktitle = "Elliptic Curves, Modular Forms and Iwasawa Theory",

}