Constructible exponential functions, motivic Fourier transformation and transfer principle. (Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de transfert). (French) Zbl 1081.14032

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.


14G20 Local ground fields in algebraic geometry
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