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

In previous work, the authors defined a category SModF 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 SModK SMod K to SModF 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.