Period Domains over Finite and p-adic Fields

A systematic exposition of the basics of period domains. Suitable for advanced graduate students.

Jean-François Dat (Author), Sascha Orlik (Author), Michael Rapoport (Author)

9780521197694, Cambridge University Press

Hardback, published 8 July 2010

396 pages
22.9 x 15.2 x 2.5 cm, 0.7 kg

'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 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.

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.

Subject Areas: Number theory [PBH], Mathematics [PB]