p-Adic Lie Groups

  • Peter Schneider

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 344)

Table of contents

  1. Front Matter
    Pages I-XI
  2. p-Adic Analysis and Lie Groups

    1. Front Matter
      Pages 1-1
    2. Peter Schneider
      Pages 3-43
    3. Peter Schneider
      Pages 45-88
    4. Peter Schneider
      Pages 89-153
  3. The Algebraic Theory of p-Adic Lie Groups

    1. Front Matter
      Pages 155-155
    2. Peter Schneider
      Pages 157-167
    3. Peter Schneider
      Pages 169-194
    4. Peter Schneider
      Pages 195-217
    5. Peter Schneider
      Pages 219-250
  4. Back Matter
    Pages 251-254

About this book

Introduction

Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

Keywords

22E20, 16S34 Lie group completed group ring locally analytic manifold p-adic p-valuation

Authors and affiliations

  • Peter Schneider
    • 1
  1. 1., Institute of MathematicsUniversity of MünsterMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-21147-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21146-1
  • Online ISBN 978-3-642-21147-8
  • Series Print ISSN 0072-7830
  • About this book