Constructible exponential functions, motivic Fourier transform and transfer principle

By Raf Cluckers, François Loeser. 2005

115 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/31239c4ff3618d4c3ca99355bbd9a0e2865e4ff6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Raf Cluckers
2. François Loeser
3. Johannes Nicaise
4. Siegfried M. Rump
5. Nicolas Templier
6. S. Shin
7. Leonard Lipshitz
8. Willem Veys

In Mathematical Physics

1. Raf Cluckers
2. François Loeser
3. Johannes Nicaise
4. Nicolas Templier
5. S. Shin
6. Leonard Lipshitz
7. G. Fichou

Citations in the corpus

• Constructible motivic functions and motivic integration (2004, background): “AG/0410203, we have been able to extend our work to the exponential setting and to prove a general “Transfer principle” à la Ax–Kochen–Eršov in this context [9], [10].”
• Transfer Principle for the Fundamental Lemma (2007, background): “1 (Specialization, Cluckers-Loeser [9] [10]).”