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.
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.
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.