Motivic integration and its interactions with model theory and non-Archimedean geometry

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Motivic integration and its interactions with model theory and non-Archimedean geometry

edited by Raf Cluckers, Johannes Nicaise, Julien Sebag

（London Mathematical Society lecture note series, 383-384）

Cambridge University Press, 2011

  • v. 1 : pbk
  • v. 2 : pbk

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Includes bibliographical references

Description and Table of Contents

Volume

v. 1 : pbk ISBN 9780521149761

Description

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 first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces.

Table of Contents

  • 1. Introduction Raf Cluckers, Johannes Nicaise and Julien Sebag
  • 2. Introduction to the model theory of valued fields Zoe Chatzidakis
  • 3. On the definition of rigid analytic spaces Siegfried Bosch
  • 4. Topological rings in rigid geometry Fumiharu Kato
  • 5. The Grothendieck ring of varieties Johannes Nicaise and Julien Sebag
  • 6. A short course on geometric motivic integration Manuel Blickle
  • 7. Motivic invariants of rigid varieties and applications to complex singularities Johannes Nicaise and Julien Sebag
  • 8. Motivic integration in mixed characteristic with bounded ramification: a summary Raf Cluckers and Francois Loeser.
Volume

v. 2 : pbk ISBN 9781107648814

Description

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.

Table of Contents

  • Preface
  • 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 Francoise 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 Roekaeus
  • 7. Absolute desingularization in characteristic zero Michael Temkin.

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