On equivariant derived categories
We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. In particular, we discuss decompositions of the equivariant category, prove the existence of a Serre functor, and give a criterion for the equivariant cat...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
11 May 2023
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| In: |
European journal of mathematics
Year: 2023, Volume: 9, Issue: 2, Pages: 1-39 |
| ISSN: | 2199-6768 |
| DOI: | 10.1007/s40879-023-00635-y |
| Online Access: | Resolving-System, kostenfrei, Volltext: https://doi.org/10.1007/s40879-023-00635-y Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s40879-023-00635-y 
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| Author Notes: | Thorsten Beckmann, Georg Oberdieck |
| Summary: | We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. In particular, we discuss decompositions of the equivariant category, prove the existence of a Serre functor, and give a criterion for the equivariant category to be Calabi-Yau. We describe an obstruction for a subgroup of the group of auto-equivalences to act on the derived category. As application we show that the equivariant category of any Calabi-Yau action on the derived category of an elliptic curve is equivalent to the derived category of an elliptic curve. |
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| Item Description: | Gesehen am 11.12.2024 |
| Physical Description: | Online Resource |
| ISSN: | 2199-6768 |
| DOI: | 10.1007/s40879-023-00635-y |