论文标题
完全交叉路口的完全无环复合物的关键和统治程度
The Critical and Cocritical Degrees of a Totally Acyclic Complex over a Complete Intersection
论文作者
论文摘要
众所周知，在完整的相交环上，模块的最小自由分辨率最终在其贝蒂序列中产生了不错的图案。 1997年，Avramov，Gasharov和Peeva定义了有限生成的模块的临界程度的概念，证明每当模块具有有限的CI量度时，该程度都是有限的。本文通过完整的分辨率扩展了关键程度的概念，从而在完全相交的环上定义了对象的关键和统一程度。特别是，我们提供了适当的对临界程度的双重类似物，使我们能够为复合物引入一种称为临界直径的新措施。
It is widely known that the minimal free resolution of a module over a complete intersection ring has nice patterns eventually arising in its Betti sequence. In 1997, Avramov, Gasharov, and Peeva defined the notion of critical degree for finitely generated modules, proving that this degree is finite whenever the module has finite CI-dimension. This paper extends the notion of critical degree via complete resolutions, thus defining the critical and cocritical degrees of an object in the category of totally acyclic complexes over a complete intersection ring of the form $R=Q/(f_1,\dots,f_c)$. In particular, we provide the appropriate dual analogue to critical degree which enables us to introduce a new measure for complexes, called the critical diameter.
