Structure of semisimple differentials and p-class groups in \({\mathbb{Z}}_ p\)-extensions
type: Item
instance of: scholarly article
title: Structure of semisimple differentials and p-class groups in \({\mathbb{Z}}_ p\)-extensions
zbMATH Open document ID: 0596.12007
DOI: 10.1007/BF01437486
author: Manohar L. Madan
author: Gabriel D. Villa Salvador
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155200
review text: 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.
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 3959568
zbMATH Keywords: algebraic function fields
zbMATH Keywords: holomorphic semisimple differentials
zbMATH Keywords: p- extensions of \({\mathbb{Z}}_ pfields\) of CM-type
zbMATH Keywords: p-class group
MaRDI profile type: Publication
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OpenAlex ID: W2089694627
description: scientific article; zbMATH DE number 3959568