论文标题
蜂窝分辨率的家族，它们的syzygies和稳定性
Families of cellular resolutions, their syzygies, and stability
论文作者
论文摘要
我们通过将其视为类别并应用表示稳定性的工具来研究细胞分辨率的家庭。我们获得有关家庭结构的足够条件，可以将其具有noetherian代表类别，并将其应用于家庭的具体例子。在对Syzygies的研究中，我们利用将Syzygy模块定义为表示该表示有限生成的条件。然后，我们表明，许多来自理想力量的蜂窝分辨率家族都满足了这些条件，并具有有限的共同体，包括最大的理想和路径的边缘理想。
We study families of cellular resolutions by looking at them as a category and applying tools from representation stability. We obtain sufficient conditions on the structure of the family to have a noetherian representation category and apply this to concrete examples of families. In the study of syzygies we make use of defining the syzygy module as a representation and find conditions for the finite generation of this representation. We then show that many families of cellular resolutions coming from powers of ideals satisfy these conditions and have finitely generated syzygies, including the maximal ideals and edge ideals of paths.
