Maximal Cohen-Macaulay complexes and their uses: A partial survey
Maximal Cohen-Macaulay complexes and their uses: A partial survey
复制标题
最大科恩-麦考利复合体及其用途：部分调查
DOI：
10.1007/978-3-030-89694-2_15
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Iyengar, Srikanth B.
中科院分区：
文献类型：
--
作者：
Iyengar, Srikanth B.
本文引入了交换Noether局部环上的最大深度复形和最大Cohen-Macaulay复形的概念。这种复合物的存在与Hochster的“同调结构”密切相关，其中大部分最近由André解决。描述了极大Cohen-Macaulay复形的各种构造，并应用它们的存在性给出了一些同调代数的新证明，以及双有理几何中的某些结果。
This work introduces a notion of complexes of maximal depth, and maximal Cohen-Macaulay complexes, over a commutative noetherian local ring. The existence of such complexes is closely tied to the Hochster’s “homological conjectures”, most of which were recently settled by André. Various constructions of maximal Cohen-Macaulay complexes are described, and their existence is applied to give new proofs of some of the homological conjectures, and also of certain results in birational geometry.