Motivic Integration and its Interactions with Model Theory by Raf Cluckers,Johannes Nicaise,Julien Sebag

By Raf Cluckers,Johannes Nicaise,Julien Sebag

the advance of Maxim Kontsevich's preliminary principles on motivic integration has all of sudden prompted many different parts of arithmetic, starting from the Langlands application over harmonic research, to non-Archimedean research, singularity concept and birational geometry. This ebook assembles different theories of motivic integration and their purposes for the 1st time, permitting readers to check assorted ways and investigate their person strengths. all the priceless history is equipped to make the ebook available to graduate scholars and researchers from algebraic geometry, version thought and quantity concept. purposes in numerous components are integrated in order that readers can see motivic integration at paintings in different domain names. In a rapidly-evolving quarter of study this booklet will end up important. this primary quantity comprises introductory texts at the version conception of valued fields, diversified ways to non-Archimedean geometry, and motivic integration on algebraic types and non-Archimedean spaces.

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