The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes
The Singularity Category Of An Exact Category Applied To Characterize Gorenstein Schemes
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DOI：
10.1093/qmath/haac013
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发表时间：
2020-09
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影响因子：
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通讯作者：
Lars Christensen;Nanqing Ding;S. Estrada;Jiangsheng Hu;Huanhuan Li;Peder Thompson
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作者：
Lars Christensen;Nanqing Ding;S. Estrada;Jiangsheng Hu;Huanhuan Li;Peder Thompson
我们构造了 Gorenstein 局部环的奇点范畴的非仿射类似物。这样，Buchweitz 在 Gorenstein 局部环上的三个三角类别的经典等价已被推广到计划中，这是 Murfet 和 Salarian 十多年前启动的一个项目。我们的构建源于我们为精确类别的奇点类别开发的框架。作为该框架在非交换设置中的应用，我们描述了有限有限维数的环。
We construct a non-affine analogue of the singularity category of a Gorenstein local ring. With this, Buchweitz’s classic equivalence of three triangulated categories over a Gorenstein local ring has been generalized to schemes, a project started by Murfet and Salarian more than ten years ago. Our construction originates in a framework we develop for singularity categories of exact categories. As an application of this framework in the non-commutative setting, we characterize rings of finite finitistic dimension.