Integration in valued fields

Ehud Hrushovski, David Kazhdan

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

78 Scopus citations

Abstract

We develop a theory of integration over valued fields of residue characteristic zero. In particular, we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef, Loeser, and Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure-preserving bijections.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages261-405
Number of pages145
DOIs
StatePublished - 2006

Publication series

NameProgress in Mathematics
Volume253
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Bibliographical note

Publisher Copyright:
© 2006, Springer Basel. All rights reserved.

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