Produktdetaljer
<p>From the reviews:</p><p>“The book is divided into two parts … . The author’s style of writing is elegant … . this is a demanding book, but a rewarding one … . any person who intends to work in this area will want to have it close at hand.” (Mark Hunacek, The Mathematical Gazette, Vol. 98 (541), March, 2014)</p><p>“This book presents the foundations of the theory of p-adic Lie groups in a systematic and self-contained way. … Schneider’s book on p-adic Lie groups systematically develops the analytic theory of p-adic Lie groups and also Lazard’s algebraic approach to p-adic Lie groups. It is highly recommended.” (Dubravka Ban, Mathematical Reviews, Issue 2012 h)</p><p>“The notion of a p-adic Lie group has been around for a while, but they have recently become more prominent in number theory and representation theory. … Schneider’s Grundlehren volume is an attempt to fill that gap by giving a systematic treatment of the subject. … this is a book to be welcomed and studied carefully by anyone who wants to learn about p-adic Lie theory.” (Fernando Q. Gouvêa, The Mathematical Association of America, August, 2011)</p><p>“The book thoroughly discusses the analytic aspects of p-adic manifolds and p-adic lie groups. … this clearly written book by Schneider will be very useful … to all those interested learning the basic theory of p-adic groups or about the completed group ring of a p-adic group with number theoretical applications in mind.” (Bala Sury, Zentralblatt MATH, Vol. 1223, 2011)</p>
Introduction.- Part A: p-Adic Analysis and Lie Groups.- I.Foundations.- I.1.Ultrametric Spaces.- I.2.Nonarchimedean Fields.- I.3.Convergent Series.- I.4.Differentiability.- I.5.Power Series.- I.6.Locally Analytic Functions.- II.Manifolds.- II.7.Charts and Atlases.- II.8.Manifolds.- II.9.The Tangent Space.- II.10.The Topological Vector Space C^an(M,E), part 1.- II.11 Locally Convex K-Vector Spaces.- II.12 The Topological Vector Space C^an(M,E), part 2.- III.Lie Groups.- III.13.Definitions and Foundations.- III.14.The Universal Enveloping Algebra.- III.15.The Concept of Free Algebras.- III.16.The Campbell-Hausdorff Formula.- III.17.The Convergence of the Hausdorff Series.- III.18.Formal Group Laws.- Part B:The Algebraic Theory of p-Adic Lie Groups.- IV.Preliminaries.- IV.19.Completed Group Rings.- IV.20.The Example of the Group Z^d_p.- IV.21.Continuous Distributions.- IV.22.Appendix: Pseudocompact Rings.- V.p-Valued Pro-p-Groups.- V.23.p-Valuations.- V.24.The free Group on two Generators.- V.25.The Operator P.- V.26.Finite Rank Pro-p-Groups.- V.27.Compact p-Adic Lie Groups.- VI.Completed Group Rings of p-Valued Groups.- VI.28.The Ring Filtration.- VI.29.Analyticity.- VI.30.Saturation.- VII.The Lie Algebra.- VII.31.A Normed Lie Algebra.- VII.32.The Hausdorff Series.- VII.33.Rational p-Valuations and Applications.- VII.34.Coordinates of the First and of the Second Kind.- References.- Index.