A motivic change of variables formula for Artin stacks

Abstract

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 $\mathcal{X}$. With a view toward the study of stringy Hodge numbers, this change of variables formula leads to a new notion of crepantness for the map $\mathcal{X}\to Y$ that coincides with the usual notion in the special case that $\mathcal{X}$ is a scheme.

References in corpus (9)

• A New Cohomology Theory for Orbifold
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Noetherian approximation of algebraic spaces and stacks
• Twisted jets, motivic measure and orbifold cohomology
• Combinatorial constructions of derived equivalences
• The Grothendieck group of algebraic stacks
• Representability of Hilbert schemes and Hilbert stacks of points
• Very fast, very functorial, and very easy resolution of singularities
• Stringy invariants and toric Artin stacks

Cited by in corpus (1)

• Logarithmic resolution via multi-weighted blow-ups