Title: Constructible exponential functions, motivic Fourier transform and transfer principle
Authors: Cluckers, Raf ×
Loeser, Francois #
Issue Date: Mar-2010
Publisher: Annal mathematics
Series Title: Annals of mathematics vol:171 issue:2 pages:1011-1065
Abstract: 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.
ISSN: 0003-486X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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