报告题目：Noncommutative pre-resolutions of noncommutative isolated singularities
报 告人: 何济位 教授 （杭州师范大学）
摘要：In this talk, I will introduce the notion of right pre-resolutions (quasi-resolutions) for noncommutative isolated singularities, which is a weaker version of quasi-resolutions introduced by Qin-Wang-Zhang. Right quasi-resolutions for noetherian bounded below and locally finite graded algebra with right injective dimension 2 are always Morita equivalent. It is also proved that a noncommutative isolated singularity always admits a right pre-resolution. Besides, a method to verify whether a noncommutative quadric hypersurface is an isolated singularity is provided. An example of noncommutative quadric hypersurfaces with detailed computations of indecomposable maximal Cohen-Macaulay modules and right pre-resolutions is included as well.