Dualizing complexes and perverse modules over differential algebras
Dualizing complexes and perverse modules over differential algebras
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DOI：
10.1112/s0010437x04001307
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发表时间：
2003-01
影响因子：
1.8
通讯作者：
Amnon Yekutieli;James J. Zhang
中科院分区：
文献类型：
--
作者：
Amnon Yekutieli;James J. Zhang
域$\mathbb{k}$上的有限型微分代数是一个过滤代数A，使得相关的分级代数在其中心上是有限的，并且该中心是一个有限生成的$\mathbb{k}$-代数。典型的例子是光滑仿射变量上的微分算子代数，当$\text{char}\mathbb{k} = 0$。研究有限型微分代数的同调性质和几何性质。研究了该类代数A上的刚性对偶复合体的存在性、结构和方差性质。我们还定义和研究了反常A模，并证明了它们与A的刚性对偶复合体的Auslander性质的关系。
A differential algebra of finite type over a field $\mathbb{k}$ is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated $\mathbb{k}$-algebra. The prototypical example is the algebra of differential operators on a smooth affine variety, when $\text{char}\mathbb{k} = 0$. We study homological and geometric properties of differential algebras of finite type. The main results concern the rigid dualizing complex over such an algebra A: its existence, structure and variance properties. We also define and study perverse A-modules, and show how they are related to the Auslander property of the rigid dualizing complex of A.