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

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.

• 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.

"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