Quasiexcellence implies strong generation
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Ko Aoki
Abstract
We prove that the bounded derived category of coherent sheaves on a quasicompact separated quasiexcellent scheme of finite dimension has a strong generator in the sense of Bondal–Van den Bergh. This simultaneously extends two results of Iyengar–Takahashi and Neeman and is new even in the affine case. The main ingredient includes Gabber’s weak local uniformization theorem and the notions of boundedness and descendability of a morphism of schemes.
Acknowledgements
I would like to thank Shane Kelly for introducing [11] to me, and Amnon Neeman and Michael Temkin for answering several questions. I also thank Amnon, Greg Stevenson, and an anonymous referee for helpful feedback on previous versions of this paper.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces
- A support theorem for\break the Hitchin fibration: The case of GLn and KC
- Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
- Quasiexcellence implies strong generation
- Serre–Tate theory for Calabi–Yau varieties
- Vanishing and estimation results for Hodge numbers
- Torus actions, maximality, and non-negative curvature
- Local-to-global Urysohn width estimates
Articles in the same Issue
- Frontmatter
- Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces
- A support theorem for\break the Hitchin fibration: The case of GLn and KC
- Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
- Quasiexcellence implies strong generation
- Serre–Tate theory for Calabi–Yau varieties
- Vanishing and estimation results for Hodge numbers
- Torus actions, maximality, and non-negative curvature
- Local-to-global Urysohn width estimates
