论文标题
Nakayama函数及其完成Gorenstein代数的完成
The Nakayama functor and its completion for Gorenstein algebras
论文作者
论文摘要
研究了对其中心有限且投影的戈伦斯坦代数的双重性能。使用注射模块的同型类别，证明有一个局部二元定理，用于此类代数的无环络合物的子类别，类似于Grothendieck and Serre的局部双重性定理，在通知代数和代数的几何上的上下文中。一个关键的成分是Gorenstein代数的有界派生类别的Nakayama函子，及其扩展到整个Injemotopy类别的注射模块类别。
Duality properties are studied for a Gorenstein algebra that is finite and projective over its center. Using the homotopy category of injective modules, it is proved that there is a local duality theorem for the subcategory of acyclic complexes of such an algebra, akin to the local duality theorems of Grothendieck and Serre in the context of commutative algebra and algebraic geometry. A key ingredient is the Nakayama functor on the bounded derived category of a Gorenstein algebra, and its extension to the full homotopy category of injective modules.
