Related papers: Evaluation of motivic functions, non-nullity, and …
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 define a motivic measure on the Berkovich analytification of an algebraic variety defined over a trivially valued field, and introduce motivic integration in this setting. The construction is geometric with a similar spirit as…
Through a cascade of generalizations, we develop a theory of motivic integration which works uniformly in all non-archimedean local fields of characteristic zero, overcoming some of the difficulties related to ramification and small residue…
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.
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 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…
These are notes of a series of talks about motivic integration I gave on the M\"unster Model Theory Month. Readers are assumed to have some basic knowledge of model theory and of valued fields. The notes are closest to the Cluckers-Loeser…
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 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 notions of integrable functions within the theory of schemic motivic integration.
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 put forward in this paper a uniform narrative that weaves together several variants of Hrushovski-Kazhdan style integral, and describe how it can facilitate the understanding of the Denef-Loeser motivic Milnor fiber and closely related…
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…
A survey of work on motivic integration.
We develop the Denef-Loeser motivic integration to the equivariant motivic integration and use it to prove the full integral identity conjecture for regular functions.
We construct a new motivic integration morphism, the so-call bounded integral, that interpolates both the integration morphisms with and without volume forms of Hrushovski and Kazhdan. This is done within the framework of model theory of…
We introduce a new notion of $\boxast$-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and commuting with the limit of rational series. In the same…
Thanks to Hrushovski-Loeser's work on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom-Sebastiani theorem in the case of regular functions. Moreover, slightly extending of Hrushovski-Loeser's construction adjusted…
A functional equation for the motivic integral corresponding to the Milnor number of an arc is derived using the Denef-Loeser formula for the change of variables. Its solution is a function of five auxiliary parameters, it is unique up to…