p-Adic Lie Groups

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.

Year

2011

Language

English

Series

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 344

Publisher

Springer-Verlag Berlin Heidelberg

Editions

1

Pages

254

ISBN

9783642211461

Data source: Wikidata