Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1

An overview of different theories of motivic integration and their applications.

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

9780521149761, Cambridge University Press

Paperback, published 22 September 2011

346 pages, 2 b/w illus.
22.8 x 15.2 x 1.9 cm, 0.51 kg

"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

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.

1. Introduction Raf Cluckers, Johannes Nicaise and Julien Sebag
2. Introduction to the model theory of valued fields Zoé 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 François Loeser.

Subject Areas: Algebra [PBF], Mathematical logic [PBCD]