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The yoga of the Cassels–Tate pairing

Published online by Cambridge University Press:  01 November 2010

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.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2010

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