Cluckers, Raf; Loeser, François Constructible exponential functions, motivic Fourier transformation and transfer principle. (Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de transfert). (French) Zbl 1081.14032 C. R., Math., Acad. Sci. Paris 341, No. 12, 741-746 (2005). Summary: We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get various inversion statements. We define also motivic Schwartz–Bruhat spaces on which motivic Fourier transformation induces an isomorphism. Our motivic integrals specialize to non-Archimedian integrals. We give a general transfer principle comparing identities between functions defined by integrals over local fields of characteristic zero, resp. positive, having the same residue field. Details of constructions and proofs will be given elsewhere. Cited in 2 ReviewsCited in 8 Documents MSC: 14G20 Local ground fields in algebraic geometry PDF BibTeX XML Cite \textit{R. Cluckers} and \textit{F. Loeser}, C. R., Math., Acad. Sci. Paris 341, No. 12, 741--746 (2005; Zbl 1081.14032) Full Text: DOI arXiv OpenURL References: [1] Cluckers, R.; Loeser, F., Fonctions constructibles et intégration motivique. I, C. R. math. acad. sci. Paris, ser. I, 339, 411-416, (2004) · Zbl 1062.14030 [2] Cluckers, R.; Loeser, F., Fonctions constructibles et intégration motivique. II, C. R. math. acad. sci. Paris, ser. I, 339, 487-492, (2004) · Zbl 1064.14021 [3] Cluckers, R.; Loeser, F., Constructible motivic functions and motivic integration · Zbl 1179.14011 [4] Cluckers, R.; Loeser, F., Ax – kochen – eršov theorems for p-adic integrals and motivic integration, (), 109-137 · Zbl 1159.12314 [5] Cunningham, C.; Hales, T., Good orbital integrals, Represent. theory, 8, 414-457, (2004) · Zbl 1054.22016 [6] Jacquet, H., Kloosterman identities over a quadratic extension, Ann. of math., 160, 755-779, (2004) · Zbl 1071.11026 [7] Jacquet, H.; Ye, Y., Relative Kloosterman integrals for \(\operatorname{GL}(3)\), Bull. soc. math. France, 120, 263-295, (1992) · Zbl 0785.11032 [8] Laumon, G.; Ngô, B.C., Le lemme fondamental pour LES groupes unitaires · Zbl 1179.22019 [9] Ngô, B.C., Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de Jacquet et ye, Ann. sci. école norm. sup. (4), 32, 619-679, (1999) · Zbl 1002.11046 [10] Pas, J., Uniform p-adic cell decomposition and local zeta functions, J. reine angew. math., 399, 137-172, (1989) · Zbl 0666.12014 [11] J.-L. Waldspurger, Endoscopie et changement de caractéristiques, Preprint, 2004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.