论文标题
长度3的DG结构将复合物和应用到TOR代数
DG Structure on Length 3 Trimming Complexes and Applications to Tor Algebras
论文作者
论文摘要
在本文中，我们考虑了与数据相关的迭代修剪复合物，该复合物的长度为$ 3 $。我们根据相关输入数据的代数结构来计算该复合物中的显式代数结构。此外，已经表明，这些产品中的许多产品在同源性下降后变得琐碎。我们将这些结果应用于$ 3 $完美理想的Tor-Algebras的可靠性问题，并表明在轻度假设下，“修剪”理想保留的过程可保留Tor-Algebra类。特别是，我们在任意的常规本地环中构建新的理想类别，定义圆环$ g（r）$和$ h（p，q）$用于一组规定的同源数据。
In this paper, we consider the iterated trimming complex associated to data yielding a complex of length $3$. We compute an explicit algebra structure in this complex in terms of the algebra structures of the associated input data. Moreover, it is shown that many of these products become trivial after descending to homology. We apply these results to the problem of realizability for Tor-algebras of grade $3$ perfect ideals, and show that under mild hypotheses, the process of "trimming" an ideal preserves Tor-algebra class. In particular, we construct new classes of ideals in arbitrary regular local rings defining rings realizing Tor-algebra classes $G(r)$ and $H(p,q)$ for a prescribed set of homological data.
