Field change for the Cassels-Tate pairing and applications to class groups

Adam Morgan; Alexander Smith

paper

Field change for the Cassels-Tate pairing and applications to class groups

arXiv:2206.13403

Abstract

In previous work, the authors defined a category $S M o d_{F}$ of finite Galois modules decorated with local conditions for each global field $F$ . In this paper, given an extension $K / F$ of global fields, we define a restriction of scalars functor from $S M o d_{K}$ to $S M o d_{F}$ and show that it behaves well with respect to the Cassels-Tate pairing. We apply this work to study the class groups of global fields in the context of the Cohen-Lenstra heuristics.

This paper has been split out of the original version of arXiv:2103.08530. 44 pages, comments welcome!