报告题目：

Gorenstein homological properties and spectrum theory of category algebras

报 告 人：

汪任 博士（中国科技大学）

报告时间：

2018年04月19日 16:00--17:00

报告地点：

理学院东北楼四楼报告厅（404）

报告摘要：

For a finite EI category, we prove that its category algebra is Gorenstein if and only if the given category is projective; and that its category algebra is 1-Gorenstein if and only if the given category is free and projective. For a finite projective EI category, the stable category of Gorenstein-projective modules over the category algebra is tensor triangle equivalent to the singularity category of the category algebra. If in addition the category is free, we construct a maximal Cohen-Macaulay approximation of the trivial module, which is exactly the tensor identity of the above stable category. In this case, we prove that Gorenstein-projective modules are closed under the tensor product if and only if each morphism in the given category is a monomorphism. We compute the spectrum in the sense of Balmer of the singularity category of a finite projective EI category algebra.