Vanishing of some galois cohomology groups for elliptic curves

Tyler Lawson, Christian Wuthrich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 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 languageEnglish (US)
Title of host publicationElliptic Curves, Modular Forms and Iwasawa Theory
EditorsDavid Loeffler, Sarah Livia Zerbes
PublisherSpringer New York LLC
Pages373-399
Number of pages27
ISBN (Print)9783319450315
DOIs
StatePublished - 2016
EventConference 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 2015Mar 27 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume188
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherConference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015
CountryUnited Kingdom
CityCambridge
Period3/25/153/27/15

Keywords

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

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