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Rigid Cohomology over Laurent Series Fields

  • Christopher Lazda
  • Ambrus Pál

Part of the Algebra and Applications book series (AA, volume 21)

Table of contents

  1. Front Matter
    Pages i-x
  2. Christopher Lazda, Ambrus Pál
    Pages 1-15
  3. Christopher Lazda, Ambrus Pál
    Pages 17-69
  4. Christopher Lazda, Ambrus Pál
    Pages 71-129
  5. Christopher Lazda, Ambrus Pál
    Pages 131-171
  6. Christopher Lazda, Ambrus Pál
    Pages 173-225
  7. Back Matter
    Pages 227-267

About this book

Introduction

In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed.

The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields.

Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.

Keywords

p-adic cohomology rigid geometry local function fields weight-monodromy (φ,∇)-modules

Authors and affiliations

  • Christopher Lazda
    • 1
  • Ambrus Pál
    • 2
  1. 1.Università Degli Studi di PadovaPadovaItaly
  2. 2.Imperial College LondonLondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30951-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30950-7
  • Online ISBN 978-3-319-30951-4
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site