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.
Rezensionen / Stimmen
'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
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 75 Tables, unspecified
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 28 mm
Gewicht
ISBN-13
978-0-521-19769-4 (9780521197694)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Jean-Francois Dat is a Professor at the Universite de Paris VII. Sascha Orlik is a Professor at the Universitaet Paderborn. Michael Rapoport is a Professor at the Universitaet Bonn.
Autor*in
Universite de Paris VI (Pierre et Marie Curie)
Bergische Universitaet-Gesamthochschule Wuppertal, Germany
Rheinische Friedrich-Wilhelms-Universitaet Bonn
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.
