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2023•arXiv (Cornell University)Open access

The Cassels-Tate pairing on 2-Selmer groups of elliptic curves

Himanshu Shukla, Michael Stoll

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Abstract

We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This leads to a new proof that a pairing defined by Cassels on the 2-Selmer groups of elliptic curves agrees with the Cassels-Tate pairing.

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What this paper is about

We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This leads to a new proof that a pairing defined by Cassels on the 2-Selmer groups of elliptic curves agrees with the Cassels-Tate pairing.

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Available abstract

We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This leads to a new proof that a pairing defined by Cassels on the 2-Selmer groups of elliptic curves agrees with the Cassels-Tate pairing.

Key concepts: Pairing, Elliptic curve, Mathematics, Pure mathematics, Physics, Condensed matter physics, Superconductivity

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