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Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform

  • Reinhardt Kiehl
  • Rainer Weissauer

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 42)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Reinhardt Kiehl, Rainer Weissauer
    Pages 1-3
  3. Reinhardt Kiehl, Rainer Weissauer
    Pages 5-65
  4. Reinhardt Kiehl, Rainer Weissauer
    Pages 67-133
  5. Reinhardt Kiehl, Rainer Weissauer
    Pages 135-202
  6. Reinhardt Kiehl, Rainer Weissauer
    Pages 203-224
  7. Reinhardt Kiehl, Rainer Weissauer
    Pages 225-248
  8. Reinhardt Kiehl, Rainer Weissauer
    Pages 249-321
  9. Back Matter
    Pages 323-375

About this book

Introduction

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

  • Reinhardt Kiehl
    • 1
  • Rainer Weissauer
    • 2
  1. 1.Institut für Mathematik und InformatikUniversität MannheimMannheimGermany
  2. 2.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04576-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07472-1
  • Online ISBN 978-3-662-04576-3
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site