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PreprintarXiv licencearXiv

Bondal--Orlov reconstruction for tame stacks with trivial generic stabilizer

  • Daigo Ito
  • Noah Olander
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Abstract

We generalize the Bondal--Orlov Reconstruction Theorem to smooth, proper, tame algebraic stacks with generically trivial stabilizer, whose canonical bundles are nowhere torsion: They do not become trivial after pullback along any finite morphism from a projective curve. Our main tools are coherent Tannaka duality as proved by Lurie and by Hall and Rydh, and Grothendieck duality for proper tame stacks as developed by Hall and Priver. We additionally use the notion of nowhere torsion line bundle on a scheme to prove a version of the Bondal--Orlov Reconstruction Theorem for finite type, separated, Gorenstein schemes which are not necessarily proper, which generalizes work of Ballard, Favero, Ito, and Matsui.

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Cite

BibTeXRIS
BibTeX
@misc{ito2026bondalorlov,
  title = {{Bondal--Orlov reconstruction for tame stacks with trivial generic stabilizer}},
  author = {Daigo Ito and Noah Olander},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28867},
  eprint = {2609.28867},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28867},
}
RIS
TY  - UNPB
TI  - Bondal--Orlov reconstruction for tame stacks with trivial generic stabilizer
AU  - Daigo Ito
AU  - Noah Olander
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28867
UR  - https://arxiv.org/abs/2609.28867
AB  - We generalize the Bondal--Orlov Reconstruction Theorem to smooth, proper, tame algebraic stacks with generically trivial stabilizer, whose canonical bundles are nowhere torsion: They do not become trivial after pullback along any finite morphism from a projective curve. Our main tools are coherent Tannaka duality as proved by Lurie and by Hall and Rydh, and Grothendieck duality for proper tame stacks as developed by Hall and Priver. We additionally use the notion of nowhere torsion line bundle on a scheme to prove a version of the Bondal--Orlov Reconstruction Theorem for finite type, separated, Gorenstein schemes which are not necessarily proper, which generalizes work of Ballard, Favero, Ito, and Matsui.
ER  -