Constructible exponential functions, motivic Fourier transform and transfer principle

R. Cluckers; F. Loeser

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arXiv · math/0512022

Constructible exponential functions, motivic Fourier transform and transfer principle

R. Cluckers·F. Loeser

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Abstract

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. We also prove new results about p-adic integrals of exponential functions.

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BibTeX RIS

R. Cluckers, F. Loeser. 2005-12-01. Constructible exponential functions, motivic Fourier transform and transfer principle. https://arxiv.org/abs/math/0512022

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