论文标题
三角剖分类别中的同源有限维对物
Homologically finite-dimensional objects in triangulated categories
论文作者
论文摘要
在本文中，我们研究了给定的小型DG增强三角形类别的派生类别中的同源有限维对物体。使用这些，我们定义了三角剖分类别的反射性，HFD固定性和Gorenstein特性，并讨论毛虫的分类收缩。我们说明了几何和代数来源类别的示例的介绍，并提供了几何应用。特别是，我们应用结果来证明奇异品种的派生类别的半三相分解与其平滑类别的派生类别之间的两次试验，并在中央纤维上支撑。
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd-closedness, and the Gorenstein property for triangulated categories, and discuss crepant categorical contractions. We illustrate the introduced notions on examples of categories of geometric and algebraic origin and provide geometric applications. In particular, we apply our results to prove a bijection between semiorthogonal decompositions of the derived category of a singular variety and the derived category of its smoothing with support on the central fiber.
