On equivariant derived categories - Beckmann, Thorsten; Oberdieck, Georg (European journal of mathematics, 2023)
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.
Gesehen am 11.12.2024