Integration in valued fields

Details Integration in valued fields Integration in valued fields

2005-10-07

arxiv.org/abs/math/0510133v3

Mathematics

Algebraic Geometry

Local corrections

Scientific paper

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, 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.

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