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arXiv · 2109.09800

A motivic change of variables formula for Artin stacks

Matthew Satriano·Jeremy Usatine
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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.

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Matthew Satriano, Jeremy Usatine. 2021-09-20. A motivic change of variables formula for Artin stacks. https://arxiv.org/abs/2109.09800

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