论文标题
非共同支持，局部同时和光谱序列
Noncommutative supports, local cohomology and spectral sequences
论文作者
论文摘要
本文的目的是研究Artin和Zhang的非共同代数几何框架中的局部共同体学。非交换空间是通过在本地诺瑟里亚人或强烈本地Noetherian的Grothendieck类别的基础变化获得的。使用我们称之为基本对象及其外注射船体的内容，我们在这些类别中开发了支持和相关素数的理论。我们将理论应用于研究一般函数设置，该设置需要在基本对象的注入性船体上进行某些条件，并为我们提供了与局部共同体学对象相关的派生函数的频谱序列，以及一般的局部共同体以及广义的Nagata理想变换。
The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or strongly locally noetherian. Using what we call elementary objects and their injective hulls, we develop a theory of supports and associated primes in these categories. We apply our theory to study a general functorial setup that requires certain conditions on the injective hulls of elementary objects and gives us spectral sequences for derived functors associated to local cohomology objects, as well as generalized local cohomology and also generalized Nagata ideal transforms.
