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PreprintCC BY-NC-SA 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{loeser2026orbifold,
  title = {{An orbifold formula for algebraic stacks}},
  author = {François Loeser and Arthur Forey and Dimitri Wyss},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10379},
  eprint = {2609.10379},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10379},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - An orbifold formula for algebraic stacks
AU  - François Loeser
AU  - Arthur Forey
AU  - Dimitri Wyss
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10379
UR  - https://arxiv.org/abs/2609.10379
AB  - 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.
ER  -