Period Domains over Finite and p-adic Fields
Period Domains over Finite and <I>p</I>-adic Fields
Sascha Orlik, Bergische Universität-Gesamthochschule Wuppertal, Germany
Michael Rapoport, Rheinische Friedrich-Wilhelms-Universität Bonn
$170.00
USDThis 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.
- Contains complete proofs of the basics of the theory
- Brings together tools from various branches of algebra and geometry
- Provides a basis for future research
Reviews & endorsements
"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
Product details
August 2010Hardback
9780521197694
396 pages
229 × 152 × 25 mm
0.7kg
Available
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.
