Geodesic
Constructible exponential functions, motivic Fourier transform and transfer principle
Raf Cluckers1 ; François Loeser2
1 Katholieke Universiteit Leuven<br/>Departement Wiskunde<br/>Celestijnenlaan 200B<br/>B-3001 Leuven<br/>Belgium
2 École Normale Supérieure<br/>45, rue d’Ulm<br/>F-75230 Paris Cedex 05<br/>France
Annals of mathematics, Tome 171 (2010) no. 2, pp. 1011-1065.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative settings. This allows us to define a motivic Fourier transformation for which we get various inversion statements. We also define spaces of motivic Schwartz-Bruhat functions on which motivic Fourier transformation induces isomorphisms. Our motivic integrals specialize to nonarchimedean integrals. We give a general transfer principle comparing identities between functions defined by exponential integrals over local fields of characteristic zero, resp. of positive characteristic, having the same residue field. We also prove new results about $p$-adic integrals of exponential functions and stability of this class of functions under $p$-adic integration.
DOI : 10.4007/annals.2010.171.1011

Raf Cluckers 1 ; François Loeser 2

1 Katholieke Universiteit Leuven<br/>Departement Wiskunde<br/>Celestijnenlaan 200B<br/>B-3001 Leuven<br/>Belgium
2 École Normale Supérieure<br/>45, rue d’Ulm<br/>F-75230 Paris Cedex 05<br/>France 
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     title = {Constructible exponential functions, motivic {Fourier} transform and transfer principle},
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Raf Cluckers; François Loeser. Constructible exponential functions, motivic Fourier transform and transfer principle. Annals of mathematics, Tome 171 (2010) no. 2, pp. 1011-1065. doi : 10.4007/annals.2010.171.1011. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.1011/

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