Related papers: Fonctions constructibles et int\'egration motiviqu…
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…
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…
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…
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 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…
We develop the theory of motivic integration for formal schemes
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…
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 (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate…
We show that in the functional integral formalism of U(1) gauge field theory some formal manipulation such as interchange of order of integration can yield erroneous results. The example studied is analysed by Fubini theorem.
Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of considering fibers, a construction dating to Berger and…
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…
We construct a quasi-categorically enhanced Grothendieck six-functor formalism on schemes of finite type over the complex numbers. In addition to satisfying many of the same properties as M. Saito's derived categories of mixed Hodge…
We study Lebesgue integration of sums of products of globally subanalytic functions and their logarithms, called constructible functions. Our first theorem states that the class of constructible functions is stable under integration. The…
We develop notions of integrable functions within the theory of schemic motivic integration.
We prove in this paper the original version of Kontsevich and Soibelman's motivic integral identity conjecture for formal functions by developing a novel framework for equivariant motivic integration on special rigid varieties. This theory…
Under a slightly stronger hypothesis, one improves a connectedness result of Debarre [D] for a product of two projective spaces in terms of the extension problem of formal-rational functions (see Theorems 1.3 and 1.4 of the introduction)
In this note, we discuss several aspects of the functoriality of universal abelian factorizations associated to representations of quivers into abelian categories. After recalling the general construction of universal abelian…
We link smooth Artin motives to \'etale local systems and Artin representations. We then construct the ordinary motivic t-structure on Artin motives with integral coefficients and show that the $\ell$-adic realization functor is t-exact.
In this article, we study criteria for producing six-functor formalisms and morphisms between them. One notable application is that the motivic homotopy theory of algebraic stacks is the universal six-functor functor formalism in a strong…