On an elementary Abelian \(p\)-extension of a multidimensional local field
type: Item
instance of: scholarly article
title: On an elementary Abelian \(p\)-extension of a multidimensional local field
zbMATH Open document ID: 0736.11069
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 1992-06-25T00:00:00Z
review text: Let \(F\) be an \(n\)-dimensional local field of characteristic 0 with first residue class field of prime characteristic \(p\). The author generalizes Shafarevich's canonical basis for the multiplicative group of one- dimensional local fields to the topological Milnor groups \(K_ m^{top}(F)\). Then he constructs the maximal elementary abelian \(p\)- extension of the field \(\mathbb{Q}_ p\{\{t_ 1\},\ldots,\{t_{n-1}\}\}\) by means of formal Lubin-Tate groups. Finally he generalizes a theorem of Dwork about the Artin symbol to \(n\)-dimensional local fields and applies this generalization to Kummer extensions.
Mathematics Subject Classification ID: 11S70
Mathematics Subject Classification ID: 11S31
Mathematics Subject Classification ID: 19D45
Mathematics Subject Classification ID: 11S15
Mathematics Subject Classification ID: 19F05
Mathematics Subject Classification ID: 14L05
zbMATH DE Number: 10873
zbMATH Keywords: \(n\)-dimensional local field
zbMATH Keywords: Milnor groups
zbMATH Keywords: maximal elementary abelian \(p\)-extension
zbMATH Keywords: formal Lubin-Tate groups
zbMATH Keywords: Artin symbol
zbMATH Keywords: Kummer extensions
author: S. V. Vostokov
reviewed by: Helmut Koch
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 10873