Period Domains over Finite and p-adic Fields

by Jean-François Dat, Sascha Orlik, Michael Rapoport

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.

Product Details

ISBN-13:	9780521197694
Publisher:	Cambridge University Press
Publication date:	07/08/2010
Series:	Cambridge Tracts in Mathematics , #183
Edition description:	Reissue
Pages:	396
Product dimensions:	6.10(w) x 9.00(h) x 1.10(d)

About the Author

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.

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.

Editorial Reviews

"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

From the Publisher