Spherical DG-functors
Spherical DG-functors
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DOI：
10.4171/jems/724
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发表时间：
2017-01-01
影响因子：
2.6
通讯作者：
Logvinenko, Timothy
中科院分区：
文献类型：
--
作者：
Anno, Rina;Logvinenko, Timothy
对于两个g -范畴A和B，我们定义了球形Morita拟函子A -> B的概念，构造了其相关的自等价：捻T是Aut D(B)的一个元素，捻F是Aut D(A)的一个元素。给出了拟函子为球形的充分性判据，以及与一组球形拟函子相关联的扭曲编织的充分性判据。利用dg增强三角化范畴的框架，我们将上述所有问题转化为代数变体的派生范畴之间的傅立叶-穆凯变换。这是对[ST01]中关于球形物体和[Ann07]中关于球形函子的结果的广泛推广。实际上，本文取代了[Ann07]，后者在其主要定理的证明上存在致命的缺陷。虽然这个证明在概念上是正确的，但在三角分类的框架内是不可能固定下来的。
For two DG-categories A and B we define the notion of a spherical Morita quasi-functor A -> B. We construct its associated autoequivalences: the twist T is an element of Aut D(B) and the cotwist F is an element of Aut D(A). We give sufficiency criteria for a quasi-functor to be spherical and for the twists associated to a collection of spherical quasi-functors to braid. Using the framework of DG-enhanced triangulated categories, we translate all of the above to Fourier-Mukai transforms between the derived categories of algebraic varieties. This is a broad generalization of the results on spherical objects in [ST01] and on spherical functors in [Ann07]. In fact, this paper replaces [Ann07], which has a fatal gap in the proof of its main theorem. Though conceptually correct, the proof was impossible to fix within the framework of triangulated categories.