Ax-Kochen-Er{š}ov Theorems for $p$-adic integrals and motivic integration

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72815This 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-Er{š}ov 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.27 pagesAlgebraic GeometryLogicNumber Theory14G20 (Primary) 03C10, 11S80, 11U09, 22E50 (Secondary)Ax-Kochen-Er{š}ov Theorems for $p$-adic integrals and motivic integrationtext