论文标题
代数稳定定理，用于锯齿形持久模块的衍生类别
Algebraic stability theorem for derived categories of zigzag persistence modules
论文作者
论文摘要
我们从派生类别的角度和澳大利亚砂圈的角度研究锯齿形持久模块的距离。普通持久性模块的派生类别是根据经典倾斜模块而定于任意曲折持久模块的等效的。通过这种派生的等效性，我们在任意曲折持久模块的派生类别上定义和计算距离，并证明了代数稳定性定理。我们还将距离与Botnan-LeSnick引入的纯曲折持久模块的距离进行比较，以及由于Kashiwara-schapira而引起的融化理论卷积距离。
We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander--Reiten quivers. The derived category of ordinary persistence modules is derived equivalent to that of arbitrary zigzag persistence modules, depending on a classical tilting module. Through this derived equivalence, we define and compute distances on the derived category of arbitrary zigzag persistence modules and prove an algebraic stability theorem. We also compare our distance with the distance for purely zigzag persistence modules introduced by Botnan--Lesnick and the sheaf-theoretic convolution distance due to Kashiwara--Schapira.
