On equivariant derived categories

• Verfasst von: Beckmann, Thorsten [VerfasserIn]
• Verfasst von: Oberdieck, Georg [VerfasserIn]
• Titel: On equivariant derived categories
• Verf.angabe: Thorsten Beckmann, Georg Oberdieck
• E-Jahr: 2023
• Jahr: 11 May 2023
• Umfang: 39 S.
• Fussnoten: Gesehen am 11.12.2024
• Titel Quelle: Enthalten in: European journal of mathematics
• Ort Quelle: Berlin [u.a.] : Springer, 2015
• Jahr Quelle: 2023
• Band/Heft Quelle: 9(2023), 2, Artikel-ID 36, Seite 1-39
• ISSN Quelle: 2199-6768
• DOI: doi:10.1007/s40879-023-00635-y
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 13D03
• Sach-SW: 14F05
• Sach-SW: 18E30
• Sach-SW: Derived categories
• Sach-SW: Equivariant categories
• Sach-SW: Stability conditions
• K10plus-PPN: 1911966103

Abstract

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.