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Motivic Integration

Benefits

  • Includes the first complete treatment of geometric motivic integration in a monograph

  • Covers the construction of arc schemes and Greenberg schemes

  • Provides a complete discussion of questions concerning the Grothendieck ring of varieties and its algebraic structure

Book

Part of the Progress in Mathematics book series (PM, volume 325)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 1-54
  3. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 55-151
  4. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 153-210
  5. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 211-262
  6. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 263-303
  7. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 305-361
  8. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 363-464
  9. Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages E1-E1
  10. Back Matter
    Pages 465-526

About this book

Introduction

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. 

With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since. 

Keywords

Greenberg schemes Grothendieck ring of varieties arc spaces birational invariants p-adic integration change of variables formula motivic zeta function motivic Serre invariant Igusa's Monodromy conjecture

Authors and affiliations

  1. 1.Université Paris Diderot, Sorbonne Paris CitéInstitut de Mathématiques de Jussieu-Paris Rive GaucheParisFrance
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.IrmarUniversité de Rennes 1Rennes CedexFrance

Bibliographic information

  • Book Title Motivic Integration
  • Authors Antoine Chambert-Loir
    Johannes Nicaise
    Julien Sebag
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-1-4939-7887-8
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2018
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4939-7885-4
  • Softcover ISBN 978-1-4939-9315-4
  • eBook ISBN 978-1-4939-7887-8
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XX, 526
  • Number of Illustrations 47 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
    K-Theory
  • Buy this book on publisher's site
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