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 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.
Full Product Details
Author: Raf Cluckers (Université de Lille) ,
Johannes Nicaise (Katholieke Universiteit Leuven, Belgium) ,
Julien Sebag (Université de Rennes I, France)
Publisher: Cambridge University Press
Imprint: Cambridge University Press (Virtual Publishing)
Volume: 383
ISBN: 9780511667534
ISBN 10: 0511667531
Publication Date: 07 October 2011
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Undefined
Publisher's Status: Active
Availability: Available To Order
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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
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
Author Information
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.
