Related papers: Constructible motivic functions and motivic integr…
We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative…
Following recent work of R. Cluckers and F. Loeser [Fonctions constructible et integration motivic I, C. R. Math. Acad. Sci. Paris 339 (2004) 411 - 416] on motivic integration, we develop a direct image formalism for positive constructible…
We extend the formalism of I to a global setting for which a theorem on fiber integrals and a Fubini theorem are obtained. We compare our formalism to the previous constructions of motivic integration in the geometric and arithmetic cases.
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…
We develop further the theory of integrable functions within the theory of relative simplicial motivic measures. We provide a primitive change of variables formula for this theory.
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…
We develop the theory of motivic integration for formal schemes
In this article, we study the commutativity between the pull-back and the push-forward functors on constructible functions in Cluckers--Loeser motivic integration.
We develop notions of integrable functions within the theory of schemic motivic integration.
The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef-Pas language, and its application to analytic motivic integrals and analytic integrals over…
We develop a "motivic integration" version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and obtain…
A survey of work on motivic integration.
We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function
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 p-adic integrals of a very general type depend on p.
We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.
We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety S over a field k of characteristic zero. We develop a theory of constructible effective Chow…
This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It…
This is a short announcement and summary of the results of arxiv:1111.7057, arxiv.org:1111.4405, and Appendix B to arxiv:1208.1945. In particular, we emphasize the exposition of the ideas related to model theory and motivic integration, and…
We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.
We define an operation of evaluation at a point for motivic constructible (exponential) functions from the Cluckers-Loeser framework of motivic integration and show that two such motivic functions are abstractly equal if and only if their…