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 language | English |
---|---|
Title of host publication | Progress in Mathematics |
Publisher | Springer Basel |
Pages | 261-405 |
Number of pages | 145 |
DOIs | |
State | Published - 2006 |
Publication series
Name | Progress in Mathematics |
---|---|
Volume | 253 |
ISSN (Print) | 0743-1643 |
ISSN (Electronic) | 2296-505X |
Bibliographical note
Publisher Copyright:© 2006, Springer Basel. All rights reserved.