Homological invariants of determinantal thickenings
Homological invariants of determinantal thickenings
复制标题
DOI：
--
复制
发表时间：
2017-12
期刊：
影响因子：
--
通讯作者：
Claudiu Raicu
中科院分区：
文献类型：
--
作者：
Claudiu Raicu
Tor、Ext和局部上同调模等同调不变量的研究是交换代数研究的一个重要方向。众所周知，要找到这些不变量的明确描述是非常困难的，而且常常涉及到结合其他数学领域的一系列技术。近年来，代数几何和表示理论的工具已被成功地用于揭示与行列式环相关的同调不变量的结构。本笔记的目的是概述其中的一些结果，重点放在示例上，试图澄清一些更技术性的陈述。
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve combining an array of techniques from other fields of mathematics. In recent years tools from algebraic geometry and representation theory have been successfully employed in order to shed some light on the structure of homological invariants associated with determinantal rings. The goal of this notes is to survey some of these results, focusing on examples in an attempt to clarify some of the more technical statements.