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In previous work, the authors defined a category $SMod_F$ of finite Galoismodules decorated with local conditions for each global field $F$. In thispaper, given an extension $K/F$ of global fields, we define a restriction ofscalars functor from $SMod_K$ to $SMod_F$ and show that it behaves well withrespect to the Cassels-Tate pairing. We apply this work to study the classgroups of global fields in the context of the Cohen-Lenstra heuristics.

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