Vanishing of some galois cohomology groups for elliptic curves

Tyler Lawson; Christian Wuthrich

doi:10.1007/978-3-319-45032-2_11

Vanishing of some galois cohomology groups for elliptic curves

Tyler Lawson
, Christian Wuthrich

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

12 Scopus citations

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.

Original language	English (US)
Title of host publication	Elliptic Curves, Modular Forms and Iwasawa Theory
Editors	David Loeffler, Sarah Livia Zerbes
Publisher	Springer New York LLC
Pages	373-399
Number of pages	27
ISBN (Print)	9783319450315
DOIs	https://doi.org/10.1007/978-3-319-45032-2_11
State	Published - 2016
Event	Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 - Cambridge, United Kingdom Duration: Mar 25 2015 → Mar 27 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	188
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015
Country/Territory	United Kingdom
City	Cambridge
Period	3/25/15 → 3/27/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016

Keywords

Birch and Swinnerton-Dyer conjecture
Elliptic curves
Galois cohomology
Grunwald-Wang problem

Publisher link

10.1007/978-3-319-45032-2_11

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Vanishing of some galois cohomology groups for elliptic curves. / Lawson, Tyler; Wuthrich, Christian.
Elliptic Curves, Modular Forms and Iwasawa Theory. ed. / David Loeffler; Sarah Livia Zerbes. Springer New York LLC, 2016. p. 373-399 (Springer Proceedings in Mathematics and Statistics; Vol. 188).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lawson, T & Wuthrich, C 2016, Vanishing of some galois cohomology groups for elliptic curves. in D Loeffler & SL Zerbes (eds), Elliptic Curves, Modular Forms and Iwasawa Theory. Springer Proceedings in Mathematics and Statistics, vol. 188, Springer New York LLC, pp. 373-399, Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 , Cambridge, United Kingdom, 3/25/15. https://doi.org/10.1007/978-3-319-45032-2_11

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Vanishing of some galois cohomology groups for elliptic curves

Abstract

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Other

Bibliographical note

Keywords

Publisher link

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