Ax-Kochen-Eršov Theorems for p-adic integrals and motivic integration

2004/10/08 by R. Cluckers, Cluckers, R., F. Loeser +1
Mathematics · #11S80 #11U09 #14G20 (Primary) 03C10 #22E50 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #math.AG #math.LO #math.NT #msc:03C10 #msc:11S80 #msc:11U09 #msc:14G20 #msc:22E50

paper · pdf · doi:10.48550/arxiv.math/0410223

27 pages

arxiv created 2004/10/08 · arxiv updated 2009/12/01

Abstract

This survey paper, to appear in he proceedings of the Miami Winter School ``Geometric Methods in Algebra and Number Theory'', is concerned with extending classical results à la Ax-Kochen-Eršov to p-adic integrals in a motivic setting, using the framework of constructible motivic functions we introduced in math.AG/0410203. We conclude the paper by discussing briefly the relevance of our results to the study of orbital integrals and the Fundamental Lemma.

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