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Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry

Volume 2

$57.00 ( ) USD

Part of London Mathematical Society Lecture Note Series

Antoine Chambert-Loir, Françoise Delon, Immanuel Halupczok, Florian Ivorra, Emmanuel Kowalski, Karl Rökaeus, Michael Temkin
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  • Date Published: November 2011
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781139142922

$ 57.00 USD ( )
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About the Authors
  • The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.

    • The first book to bring together the various theories of motivic integration
    • Provides all background material for readers from neighbouring fields
    • Contains applications in several fields of mathematics
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    Reviews & endorsements

    "Because of the variety of different aspects of the theory and the many areas of mathematics that come into play, a book like the present one is particularly precious for someone interested in learning about motivic integration as well as for someone- like the reviewer - who is familiar with some aspects of the theory but less with others and would like to learn more about this rich and beautiful subject."
    Tommaso De Fernex, Mathematical Reviews

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    Product details

    • Date Published: November 2011
    • format: Adobe eBook Reader
    • isbn: 9781139142922
    • contains: 11 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. Heights and measures on analytic spaces: a survey of recent results, and some remarks Antoine Chambert-Loir
    2. C-minimal structures without density assumption Françoise Delon
    3. Trees of definable sets in Zp Immanuel Halupczok
    4. Triangulated motives over Noetherian separated schemes Florian Ivorra
    5. A survey of algebraic exponential sums and some applications Emmanuel Kowalski
    6. A motivic version of p-adic integration Karl Rökaeus
    7. Absolute desingularization in characteristic zero Michael Temkin.

  • Editors

    Raf Cluckers, Université de Lille
    Raf Cluckers is a Research Associate of the CNRS at Université de Lille 1, France.

    Johannes Nicaise, Katholieke Universiteit Leuven, Belgium
    Johannes Nicaise is a Professor in the Department of Mathematics at the Katholieke Universiteit Leuven, Belgium.

    Julien Sebag, Université de Rennes I, France
    Julien Sebag is a Professor in the UFR Mathématiques at the Université de Rennes 1, France.


    Antoine Chambert-Loir, Françoise Delon, Immanuel Halupczok, Florian Ivorra, Emmanuel Kowalski, Karl Rökaeus, Michael Temkin

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