p-Adic Lie Groups

✍ Scribed by Peter Schneider (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 266
• Series: Grundlehren der mathematischen Wissenschaften 344
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XI
Front Matter....Pages 1-1
Foundations....Pages 3-43
Manifolds....Pages 45-88
Lie Groups....Pages 89-153
Front Matter....Pages 155-155
Preliminaries....Pages 157-167
p -Valued Pro- p -Groups....Pages 169-194
Completed Group Rings of p -Valued Groups....Pages 195-217
The Lie Algebra....Pages 219-250
Back Matter....Pages 251-254

✦ Subjects

Topological Groups, Lie Groups; Associative Rings and Algebras