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The yoga of the Cassels–Tate pairing

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 November 2010

Tom Fisher ,
Edward F. Schaefer  and
Michael Stoll
Tom Fisher
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road Cambridge CB3 0WB, United Kingdom (email: T.A.Fisher@dpmms.cam.ac.uk)
Edward F. Schaefer
Affiliation:
Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA 95053, USA (email: eschaefer@scu.edu)
Michael Stoll
Affiliation:
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany (email: Michael.Stoll@uni-bayreuth.de)

Abstract

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Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels–Tate pairing. In this article, we prove that the two pairings are the same.

MSC classification

Secondary: 11G05: Elliptic curves over global fields 11G07: Elliptic curves over local fields
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 451 - 460
Copyright
Copyright © London Mathematical Society 2010

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