Cohomological descent theory for a morphism of stacks and for equivariant derived categories
Cohomological descent theory for a morphism of stacks and for equivariant derived categories
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堆栈态射和等变派生类别的上同调下降理论
DOI：
10.1070/sm2011v202n04abeh004153
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A. Elagin
中科院分区：
文献类型：
--
作者：
A. Elagin
本文给出了用下降论的工具可以从的派生范畴恢复的代数变体（或更一般的堆栈）的态射的派生范畴的充要条件。我们证明了对于一个线性约化代数群在一个方案上的作用，这一结果暗示了在每个对象上的给定作用下-等变的滑轮的派生范畴和滑轮的派生范畴中的对象的范畴是等价的。参考书目：18篇。
In the paper, we find necessary and sufficient conditions under which, if is a morphism of algebraic varieties (or, in a more general case, of stacks), the derived category of can be recovered by using the tools of descent theory from the derived category of . We show that for an action of a linearly reductive algebraic group on a scheme this result implies the equivalence of the derived category of -equivariant sheaves on and the category of objects in the derived category of sheaves on with a given action of on each object. Bibliography: 18 titles.