The improvement of Maxim Kontsevich's preliminary rules on motivic integration has without warning stimulated many different parts of arithmetic, starting from the Langlands software over harmonic research, to non-Archimedean research, singularity concept and birational geometry. This publication assembles different theories of motivic integration and their functions for the 1st time, permitting readers to match diversified techniques and investigate their person strengths. the entire beneficial historical past is equipped to make the e-book available to graduate scholars and researchers from algebraic geometry, version concept and quantity thought. functions in numerous components are incorporated in order that readers can see motivic integration at paintings in different domain names. In a rapidly-evolving quarter of analysis this booklet will end up important. this primary quantity comprises introductory texts at the version concept of valued fields, varied methods to non-Archimedean geometry, and motivic integration on algebraic kinds and non-Archimedean areas.
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