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Motivic Integration

  • Book
  • © 2018

Overview

Authors:
  1. Antoine Chambert-Loir

    1. Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France

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  2. Johannes Nicaise

    1. Department of Mathematics, Imperial College London, London, UK

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  3. Julien Sebag

    1. Irmar, Université de Rennes 1, Rennes Cedex, France

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  • 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

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Prologue: p-Adic Integration

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 1-54

  3. The Grothendieck Ring of Varieties

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 55-151

  4. Arc Schemes

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 153-210

  5. Greenberg Schemes

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 211-262

  6. Structure Theorems for Greenberg Schemes

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 263-303

  7. Motivic Integration

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 305-361

  8. Applications

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages 363-464

  9. Correction to: Motivic Integration

    • Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
    Pages E1-E1

  10. Back Matter

    Pages 465-526
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Keywords

About this book

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. 

Authors and Affiliations

  • Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France

    Antoine Chambert-Loir

  • Department of Mathematics, Imperial College London, London, UK

    Johannes Nicaise

  • Irmar, Université de Rennes 1, Rennes Cedex, France

    Julien Sebag

Bibliographic Information

  • Book Title: Motivic Integration

  • Authors: Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4939-7887-8

  • Publisher: Birkhäuser New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2018

  • Hardcover ISBN: 978-1-4939-7885-4Published: 15 September 2018

  • Softcover ISBN: 978-1-4939-9315-4Published: 10 December 2019

  • eBook ISBN: 978-1-4939-7887-8Published: 15 September 2018

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XX, 526

  • Number of Illustrations: 47 b/w illustrations

  • Topics: Algebraic Geometry, K-Theory

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