Structure of semisimple differentials and p-class groups in \({\mathbb{Z}}_ p\)-extensions
For a wildly ramified p-extension E/F of algebraic function fields of one variable in an algebraically closed field k of characteristic p with Galois group G, Nakajima obtained two exact sequences which determined implicitly the structure of the holomorphic semisimple differentials as k[G]-module. In this paper, in many cases, e.g., if there is a fully ramified prime, the structure is determined explicitly. Analogous results are obtained for p-extensions of \({\mathbb{Z}}_ p\)-fields of CM-type. In the latter situation, if E/F is unramified, the structure of the minus part of the p-class group of E is determined as \({\mathbb{Z}}_ p[G]\)-module.
p- extensions of \({\mathbb{Z}}_ pfields\) of CM-type
scientific article; zbMATH DE number 3959568
scientific article