LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA
LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA
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DOI：
10.1017/nmj.2020.2
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发表时间：
2019-05
影响因子：
0.8
通讯作者：
D. Benson;S. Iyengar;H. Krause;J. Pevtsova
中科院分区：
文献类型：
--
作者：
D. Benson;S. Iyengar;H. Krause;J. Pevtsova
证明了有限维Gorenstein代数奇异范畴的一个对偶定理。它补充了哈佩尔发现的完美复形范畴的对偶性。其后果之一是类似的塞尔对偶，和存在的Auslander-Reiten三角形的$\mathfrak{p}$-本地和$\mathfrak{p}$-扭转子范畴的衍生类别，每个齐次素理想$\mathfrak{p}$所产生的行动，一个交换环通过Hochschild上同调。
A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the $\mathfrak{p}$-local and $\mathfrak{p}$-torsion subcategories of the derived category, for each homogeneous prime ideal $\mathfrak{p}$ arising from the action of a commutative ring via Hochschild cohomology.