Period Domains Over Finite and p-Adic Fields

Erscheinungsjahr 2011
ISBN: 978-0-521-19769-4
Verlag: Cambridge University Press

Buch, Englisch, Band 183, 396 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 792 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Dat, Jean-François

Orlik, Sascha

Rapoport, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Orlik, Sascha
Sascha Orlik is a Professor at the Universität Paderborn.

Rapoport, Michael
Michael Rapoport is a Professor at the Universität Bonn.

Dat, Jean-François
Jean-Francois Dat is a Professor at the Université de Paris VII.