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  • © 2001

Weil Conjectures, Perverse Sheaves and ℓ-adic Fourier Transform

  • Describes the important generalisation of the original Weil conjectures

  • For the first time the authors describe Deligne's work in the framework of the sheaf theoretic theory of perverse sheaves

  • The l-adic Fourier transform is introduced as a powerful tool

  • Presents important applications

  • Includes supplementary material: sn.pub/extras

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
  2. Introduction

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 1-3
  3. The General Weil Conjectures (Deligne’s Theory of Weights)

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 5-65
  4. The Formalism of Derived Categories

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 67-133
  5. Perverse Sheaves

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 135-202
  6. Lefschetz Theory and the Brylinski-Radon Transform

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 203-224
  7. Trigonometric Sums

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 225-248
  8. The Springer Representations

    • Reinhardt Kiehl, Rainer Weissauer
    Pages 249-321
  9. Back Matter

    Pages 323-375

About this book

In this book the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.

Keywords

  • Deligne's Fourier transform
  • Deline's theory of weights and of purity
  • Etale cohomology
  • Fourier transform
  • Hard Lefschetz Theorem
  • Springer representations Weyl groups
  • boundary element method
  • cohomology
  • estimates of exponential sums
  • form
  • framework
  • generalized Weil conjecture
  • middle perverse sheaves
  • proof
  • sheaves

Authors and Affiliations

  • Institut für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

    Reinhardt Kiehl

  • Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany

    Rainer Weissauer

Bibliographic Information

Buy it now

Buying options

eBook USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access