Related papers: An introduction to motivic integration
The present work is devoted to the study of motivic integration on quotient singularities. We give a new proof of a form of the McKay correspondence previously proved by Batyrev. The paper contains also some general results on motivic…
We study the McKay correspondence for representations of the cyclic group of order $p$ in characteristic $p$. The main tool is the motivic integration generalized to quotient stacks associated to representations. Our version of the change…
Let $\mathcal{X} \to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over arcs of $Y$ to motivic integrals over arcs of $\mathcal{X}$.…
The purpose of this paper is to show how the motivic integration methods of Kontsevich, Denef-Loeser and Looijenga can be adapted to prove the McKay-Ruan correspondence, a generalization of the McKay-Reid correspondence to orbifolds that…
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…
We introduce a quotient of the Grothendieck ring of varieties by identifying classes of universally homeomorphic varieties. We show that the standard realization morphisms factor through this quotient, and we argue that it is the correct…
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…
We define a motivic analogue of the Haar measure for groups of the form G(k((t))), where k is an algebraically closed field of characteristic zero, and G is a reductive algebraic group defined over k. A classical Haar measure on such groups…
We develop the motivic integration theory over formal Deligne-Mumford stacks over a power series ring of arbitrary characteristic. This is a generalization of the corresponding theory for tame and smooth Deligne-Mumford stacks constructed…
In a previous paper we showed that any variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. In this paper we prove the converse, thereby proving that a variety admits a crepant resolution by a smooth…
We prove the version of Joyce-Song formula for the Behrend function identities in the motivic setting. The main method we use is the proof of Kontsevich-Soibelman conjecture about the motivic Milnor fibers by Q. T. Le, who uses the method…
In this paper, we construct four different theories of integration, two that are for Voevodsky motives, one for mixed $\ell$-adic sheaves, and a fourth theory of integration for rational mixed Hodge structures. We then show that they…
This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.
We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.
We propose a conjectural framework for computing Gorenstein measures and stringy Hodge numbers in terms of motivic integration over arcs of smooth Artin stacks, and we verify this framework in the case of fantastacks, which are certain…
We revisit the classical two-dimensional McKay correspondence in two respects: The first one, which is the main point of this work, is that we take into account of the multiplicative structure given by the orbifold product; second, instead…
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…
Hodge correlators are complex numbers given by certain integrals assigned to a smooth complex curve. We show that they are correlators of a Feynman integral, and describe the real mixed Hodge structure on the pronilpotent completion of the…
The deepest arithmetic invariants attached to an algebraic variety defined over a number field $F$ are conjecturally captured by the integral part of its motivic cohomology. There are essentially two ways of defining it when $X$ is a smooth…
We obtain a cohomological interpretation for Batyrev's stringy Hodge numbers in the full generality in which they are defined. In a previous paper, the second and third authors used motivic integration to define the stringy Hodge--Deligne…