Abstract
We show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of "weakly symmetric" unimodular torus representations are derived equivalent. This yields evidence for a non-commutative extension of a well known conjecture by Bondal and Orlov stating that all crepant resolutions of a Gorenstein singularity are derived equivalent. We prove our result by showing that all toric NCCRs of the affine GIT quotient are derived equivalent to a fixed Deligne-Mumford GIT quotient stack associated to a generic character of the torus. This extends a result by Halpern-Leistner and Sam which showed that such GIT quotient stacks are a geometric incarnation of a family of specific toric NCCRs constructed earlier by the authors.
| Original language | English |
|---|---|
| Pages (from-to) | 1055-1068 |
| Number of pages | 14 |
| Journal | Mathematische Zeitschrift |
| Volume | 300 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2022 |
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. 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”.
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© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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Copyright 2021 Elsevier B.V., All rights reserved.