论文标题
在衍生类别上
On equivariant derived categories
论文作者
论文摘要
我们研究了与平滑投射品种的连贯滑轮类别的有限群体行动相关的均等类别。我们讨论了模棱两可的类别的分解和忠实的行动，证明了Serre函子的存在，给出了等效类别的标准，即是Calabi-Yau，并描述了对行动的自动等量组的子组的阻碍。作为应用程序，我们表明，在椭圆曲线的派生类别上任何符号动作的类别类别都等同于椭圆曲线的派生类别。
We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. We discuss decompositions of the equivariant category and faithful actions, prove the existence of a Serre functor, give a criterion for the equivariant category to be Calabi--Yau, and describe an obstruction for a subgroup of the group of auto-equivalences to act. As application we show that the equivariant category of any symplectic action on the derived category of an elliptic curve is equivalent to the derived category of an elliptic curve.
