Work

Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero

Year: 2013

Type: article

Abstract: We extend the formalism and results on motivic integration from [Invent. Math. 173 (2008), 23–121] to mixed characteristic discretely valued Henselian fields with bounded ramification. We also generalize the equicharacteristic zero case of loc. cit. by giving, in all residue characteristics, an axiomatic approach (instead of only using Denef–Pas languages) and by using richer angular component maps. In this setting we prove a general change of variables formula and a general Fubini Theorem. Our set-up can be specialized to previously known versions of motivic integration by e.g. the second author and J. Sebag and to classical p-adic integrals.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2013-0025

Authors: Raf Cluckers, François Loeser