The Cassels-Tate pairing on 2-Selmer groups of elliptic curves
Himanshu Shukla, Michael Stoll
TL;DR
This paper explicitly computes the Cassels-Tate pairing on 2-Selmer groups of elliptic curves, providing a new proof of its equivalence with Cassels' pairing using the Albanese-Albanese approach.
Contribution
It introduces an explicit computation method for the Cassels-Tate pairing on 2-Selmer groups and confirms its agreement with Cassels' original pairing.
Findings
Explicit computation of the pairing using Albanese-Albanese definition
Proof of equivalence between Cassels' pairing and Cassels-Tate pairing
New insights into the structure of 2-Selmer groups
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry