Abstract
If is a reductive group which acts on a linearized smooth scheme then we show that under suitable standard conditions the derived category of coherent sheaves of the corresponding GIT quotient stack has a semi-orthogonal decomposition consisting of derived categories of coherent sheaves of rings on the categorical quotient which are locally of finite global dimension. One of the components of the decomposition is a certain non-commutative resolution of constructed earlier by the authors. The results in this paper also complement a result by Halpern-Leistner (and similar results by Ballard-Favero-Katzarkov and Donovan-Segal) that asserts the existence of a semi-orthogonal decomposition of the derived category of in which one of the components is the derived category of
| Original language | English |
|---|---|
| Article number | 16 |
| Number of pages | 43 |
| Journal | Selecta Mathematica-New Series |
| Volume | 27 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - May 2021 |
Bibliographical note
Funding Information:Š. Špenko is a FWO [PEGASUS Marie Skłodowska-Curie fellow at the Free University of Brussels (funded by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665501 with the Research Foundation Flanders (FWO)). During part of this work she was also a postdoc with Sue Sierra at the University of Edinburgh. Partly she was supported by L’Oréal-UNESCO scholarship “For women in science”. M. Van den Bergh is a senior researcher at the Research Foundation Flanders (FWO). While working on this project he was supported by the FWO Grant G0D8616N: “Hochschild cohomology and deformation theory of triangulated categories”. Substantial progress on this project was made during visits of the authors to each other’s host institutions. They respectively thank the University of Hasselt and the University of Edinburgh for their hospitality and support.
Funding Information:
The second author thanks Jørgen Vold Rennemo and Ed Segal for interesting discussions regarding this paper. The authors thank Agnieszka Bodzenta and Alexey Bondal for their interest in this work and for useful comments on the first version of this paper. They also thank the referees for pointing out many typos and for the suggestions which improved the exposition of the paper.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.