Overview

This book is, on the one hand, a pedagogical introduction to the formalism of slopes, of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition, the end of each section includes remarks on open questions, historical context and references to the literature.

Full Product Details

Author:   Jean-François Dat (Université de Paris VI (Pierre et Marie Curie)) ,  Sascha Orlik (Bergische Universität-Gesamthochschule Wuppertal, Germany) ,  Michael Rapoport (Rheinische Friedrich-Wilhelms-Universität Bonn)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   183
ISBN:  

9780511762482

ISBN 10:   0511762488
Publication Date:   02 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   In stock  
We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately.

Table of Contents

Preface; Introduction; Part I. Period Domains for GLn Over a Finite Field: 1. Filtered vector spaces; 2. Period domains for GLn; 3. Cohomology of period domains for GLn; Part II. Period Domains for Reductive Groups over Finite Fields: 4. Interlude on the Tannakian formalism; 5. Filtrations on repk(G); 6. Period domains for reductive groups; 7. Cohomology of period domains for reductive groups; Part III. Period Domains over p-adic Fields: 8. Period domains over p-adic fields; 9. Period domains for p-adic reductive groups; 10. Cohomology of period domains over p-adic fields; Part IV. Complements: 11. Further aspects of period domains; References; Index.

Reviews

'This monograph is a systematic treatise on period domains over finite and over p-adic fields. It presents the theory as it has developed over the past fifteen years ... The book should serve as the basis of future research in this area.' Zentralblatt MATH This book gives a very detailed and pedagogical introduction to the theory of period domains over finite and p-adic fields. It should prove indispensable for every non-expert or graduate student who wants to understand current research in arithmetic geometry or number theory using this theory. Volker J. Heiermann, Mathematical Reviews

'This monograph is a systematic treatise on period domains over finite and over p-adic fields. It presents the theory as it has developed over the past fifteen years ... The book should serve as the basis of future research in this area.' Zentralblatt MATH

'This monograph is a systematic treatise on period domains over finite and over p-adic fields. It presents the theory as it has developed over the past fifteen years … The book should serve as the basis of future research in this area.' Zentralblatt MATH

Author Information

Jean-Francois Dat is a Professor at the Université de Paris VII. Sascha Orlik is a Professor at the Universität Paderborn. Michael Rapoport is a Professor at the Universität Bonn.

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions