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

Raf Cluckers, Johannes Nicaise, Julien Sebag

• Publisher: Cambridge University Press
• Year: 2011
• Print ISBN:
  9781107648814
• eBook ISBN:
  9781139142922
• Topic: Matematica
• Subtopic: Logica nella matematica

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

• Cover
• Title
• Copyright
• Table of Contents for Volume II
• List of contributors
• Preface
• 9 Heights and measures on analytic spaces. A survey of recent results, and some remarks
• 10 C-minimal structures without density assumption
• 11 Trees of definable sets in Zp
• 12 Triangulated motives over noetherian separated schemes
• 13 A survey of algebraic exponential sums and some applications
• 14 A motivic version of p-adic integration
• 15 Absolute desingularization in characteristic zero