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.
Rezensionen / Stimmen
"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
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Illustrationen
2 Line drawings, unspecified
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 19 mm
Gewicht
ISBN-13
978-0-521-14976-1 (9780521149761)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
Herausgeber*in
Universite de Lille
Katholieke Universiteit Leuven, Belgium
Universite de Rennes I, France
1. Introduction Raf Cluckers, Johannes Nicaise and Julien Sebag; 2. Introduction to the model theory of valued fields Zoe 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 Francois Loeser.
