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arXiv · 2609.10379

An orbifold formula for algebraic stacks

François Loeser·Arthur Forey·Dimitri Wyss
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Abstract

We study motivic integration on varieties that are birational to smooth algebraic stacks and prove a generalization of the orbifold formula for varieties with finite quotient singularities. This leads in particular to a new way of computing stringy E-functions and we also give applications to the study of klt-singularities. Along the way we study Cluckers-Loeser motivic integration on algebraic stacks, which might be of independent interest. The proof relies furthermore on ideas from Hrushovski-Kazhdan integration and Bruhat-Tits theory.

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François Loeser, Arthur Forey, Dimitri Wyss. 2026-09-09. An orbifold formula for algebraic stacks. https://arxiv.org/abs/2609.10379

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