论文标题
精确类别的倾斜理论
Tilting Theory in exact categories
论文作者
论文摘要
我们在任意确切类别中定义倾斜子类别以构成以下内容。首先：将倾斜子类别的现有定义统一到任意确切类别。讨论倾斜子类别的标准结果：Auslander对应关系，垂直类别的Bazzoni描述。其次：我们分别处理诱导的衍生等价问题 - 给定倾斜子类别t，我们询问垂直类别上的函数是否诱导了与t（某些）函数类别的派生等效性。我们证明了Miyashita定理的概括（这本身就是对Brenner-Butler的著名定理的概括），并以允许IDEQ倾斜子类别的足够的预测类别来表征精确的类别。特别是，如果确切的类别是Abelian，则始终实现这一目标。
We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories: Auslander correspondence, Bazzoni description of the perpendicular category. Secondly: We treat the question of induced derived equivalences separately - given a tilting subcategory T, we ask if a functor on the perpendicular category induces a derived equivalence to a (certain) functor category over T. If this is the case, we call the tilting subcategory ideq tilting. We prove a generalization of Miyashita's theorem (which is itself a generalization of a well-known theorem of Brenner-Butler) and characterize exact categories with enough projectives allowing ideq tilting subcategories. In particular, this is always fulfilled if the exact category is abelian with enough projectives.
