p-Adic Lie Groups
By: by Peter Schneider
Contributors: SpringerLink (Online service)
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics -- 344
Publisher: Springer-Verlag Berlin Heidelberg
Published: 2011
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 254
ISBN-13: 9783642211461; 9783642211478
Subjects: Mathematics; Topological groups; Algebra
Description: 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.