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

2022/06/27 by Morgan, Adam, Smith, Alexander · 1 citation
#11R34 (11R29 #11R37) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.13403

Abstract

In previous work, the authors defined a category SMod_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 SMod_K to SMod_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.

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• Decomposed Levi subgroups in BD-covers of classical groups

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