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- François Loeser
- 2008

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… (More)

- François Loeser
- 1999

Introduction Let X be an algebraic variety, not necessarily smooth, over a field k of characteristic zero. We denote by L(X) the k-scheme of formal arcs on X : K-points of L(X) correspond to formal arcs Spec K[[t]] → X, for K any field containing k. In a recent paper [8], we developped an integration theory on the space L(X) with values in M, a certain ring… (More)

We develop a theory of motivic integration for smooth rigid varieties. As an application we obtain a motivic analogue for rigid varieties of Serre's invariant for p-adic varieties. Our construction provides new geometric birational invariants of degener-ations of algebraic varieties. For degenerations of Calabi-Yau varieties, our results take a stronger… (More)

- F. Loeser
- 1995

We prove that a (globally) subanalytic function f : X ⊂ Q n p → Q p which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions f y : X y ⊂ Q n… (More)

- Riccardo Benedetti, François Loeser, Jean-Jacques Risler
- Discrete & Computational Geometry
- 1991

Motivic integration is a powerful technique to prove that certain quantities associated to algebraic varieties are birational invariants or are independent of a chosen resolution of singularities. We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how… (More)

- Jennifer Beineke, Jason Rosenhouse, +6 authors Takeshi Tsuji
- 2010

The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics. Game Theory in Action is an undergraduate textbook about using game theory across a range of real-life scenarios. From traffic accidents to the sex lives of lizards, Stephen… (More)

- François Loeser
- 2008