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Period Domains over Finite and p-adic Fields

$114.99

Part of Cambridge Tracts in Mathematics

  • Date Published: August 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521197694

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About the Authors
  • 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.

    • 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
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    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

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    Product details

    • Date Published: August 2010
    • format: Hardback
    • isbn: 9780521197694
    • length: 396 pages
    • dimensions: 229 x 152 x 25 mm
    • weight: 0.75kg
    • availability: 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.

  • Authors

    Jean-François Dat, Université de Paris VI (Pierre et Marie Curie)
    Jean-Francois Dat is a Professor at the Université de Paris VII.

    Sascha Orlik, Bergische Universität-Gesamthochschule Wuppertal, Germany
    Sascha Orlik is a Professor at the Universität Paderborn.

    Michael Rapoport, Rheinische Friedrich-Wilhelms-Universität Bonn
    Michael Rapoport is a Professor at the Universität Bonn.

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