The yoga of the Cassels-Tate pairing
Tom Fisher, Edward F. Schaefer, Michael Stoll
TL;DR
This paper proves that Cassels' pairing on the 2-Selmer group of an elliptic curve is identical to the Cassels-Tate pairing, clarifying their relationship in number theory.
Contribution
It establishes the equivalence of two pairings, resolving a long-standing question about their relationship in the context of elliptic curves.
Findings
Cassels' pairing and the Cassels-Tate pairing are the same.
The proof clarifies the structure of the 2-Selmer group.
The result impacts the understanding of elliptic curve arithmetic.
Abstract
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.
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