On binary quartics and the Cassels-Tate pairing
Number Theory
2022-09-01 v1
Abstract
We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the -Selmer group of an elliptic curve. Unlike earlier methods, our formula does not require us to solve any conics. An important role in our construction is played by a certain surface defined by a -form.
Cite
@article{arxiv.2208.14977,
title = {On binary quartics and the Cassels-Tate pairing},
author = {Tom Fisher},
journal= {arXiv preprint arXiv:2208.14977},
year = {2022}
}
Comments
15 pages, to appear in the proceedings of ANTS 2022