Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2

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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.show more

Product details

  • Electronic book text | 270 pages
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 11 b/w illus.
  • 1139142925
  • 9781139142922

Review quote

"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 Reviewsshow more

About Raf Cluckers

Raf Cluckers is a Research Associate of the CNRS at Universite de Lille 1, France. Johannes Nicaise is a Professor in the Department of Mathematics at the Katholieke Universiteit Leuven, Belgium. Julien Sebag is a Professor in the UFR Mathematiques at the Universite de Rennes 1, France.show more

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 Rokaeus; 7. Absolute desingularization in characteristic zero Michael Temkin.show more