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

by Raf Cluckers (Editor), Johannes Nicaise (Editor), Julien Sebag (Editor)

Overview

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.

Product Details

ISBN-13:	9781107648814
Publisher:	Cambridge University Press
Publication date:	09/22/2011
Series:	London Mathematical Society Lecture Note Series , #384
Pages:	262
Product dimensions:	5.90(w) x 8.90(h) x 0.60(d)

About the Author

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

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 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.

Editorial Reviews

"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

From the Publisher