The Nakayama functor and its completion for Gorenstein algebras
The Nakayama functor and its completion for Gorenstein algebras
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DOI：
10.24033/bsmf.2849
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发表时间：
2020-10
期刊：
影响因子：
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通讯作者：
S. Iyengar;H. Krause
中科院分区：
文献类型：
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作者：
S. Iyengar;H. Krause
研究了Gorenstein代数的对偶性质，该代数是有限的且在其中心上是投射的。利用内射模的同伦范畴，证明了这样一个代数的非循环复形的子范畴存在一个局部对偶定理，类似于交换代数和代数几何中Grothendieck和Serre的局部对偶定理。一个关键的成分是中山函子上的有界导范畴的Gorenstein代数，其推广到全同伦范畴的内射模。
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.