Linearisations of triangulated categories with respect to finite group actions
Linearisations of triangulated categories with respect to finite group actions
复制标题
三角类别相对于有限群作用的线性化
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
P. Sosna
中科院分区：
文献类型：
--
作者：
P. Sosna
给定有限群对三角类别的作用，我们研究在哪些条件下可以使用 DG 增强构造线性化三角类别。特别是，如果该群是平滑射影簇的自同构的有限群，并且该范畴是相干滑轮的有界派生范畴，那么我们的构造会在光滑商簇上产生相干滑轮的有界派生范畴。堆。我们还考虑张量积与扭转正则丛给出的作用以及有限群对球形物体生成的类别的作用。
Given an action of a finite group on a triangulated category, we investigate under which conditions one can construct a linearised triangulated category using DG-enhancements. In particular, if the group is a finite group of automorphisms of a smooth projective variety and the category is the bounded derived category of coherent sheaves, then our construction produces the bounded derived category of coherent sheaves on the smooth quotient variety resp. stack. We also consider the action given by the tensor product with a torsion canonical bundle and the action of a finite group on the category generated by a spherical object.