Finite Cohen-Macaulay type and smooth non-commutative schemes

Examples of degenerations of Cohen-Macaulay modules

We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations. It is proved that such degenerations over an even-dimensional simple hypersurface singularity of type $(A_n)$ are given by extensions. We also prove that all extended degenerations of maximal Cohen-Macaulay modules over a Cohen-Macaulay complete local algebra of finite representation type are obtained by iteration of extended degenerations of Auslander-Reiten sequences.

算术 Cohen-Macaulay 簇的 Cohen-Macaulay 表示型

The Cohen-Macaulay representation type of arithmetically Cohen-Macaulay varieties

本文证明射影空间中具有 Cohen-Macaulay 分次坐标环的约化闭子概形几乎都是野 Cohen-Macaulay 型，并对少数例外情形给出完全分类。

Explicit models for some stable categories of maximal Cohen-Macaulay modules

We give concrete DG-descriptions of certain stable categories of maximal Cohen-Macaulay modules. This makes in possible to describe the latter as generalized cluster categories in certain cases.

Examples of non-commutative crepant resolutions of Cohen Macaulay normal domains

Let $A$ be a Cohen-Macaulay normal domain. A non commutative crepant resolution (NCCR) of $A$ is an $A$-algebra $Γ$ of the form $Γ= End_A(M)$, where $M$ is a reflexive $A$-module, $Γ$ is maximal Cohen-Macaulay as an $A$-module and $gldim(Γ)_P = \dim A_P $ for all primes $P$ of $A$. We give bountiful examples of equi-characteristic Cohen-Macaulay normal local domains and mixed characteristic Cohen-Macaulay normal local domains having NCCR. We also give plentiful examples of affine Cohen-Macaulay normal domains having NCCR.

极小Cohen-Macaulay DG复形

Maximal Cohen-Macaulay DG-complexes

本文提出极小Cohen-Macaulay DG复形的定义，扩展了Iyengar等人关于局部环的极小Cohen-Macaulay复形的研究，并建立了具有恒定振幅的DG环的导出改进新交集定理。

关于 Weyl 代数上的 Cohen--Macaulay 模

On Cohen--Macaulay modules over the Weyl algebra

本文提出了 Weyl 代数上 Cohen--Macaulay 模的定义，并给出了 GKZ $A$-超几何 $D$-模满足 Cohen--Macaulay 性质的充分条件。

Auslander-Reiten的Cohen-Macaulay代数与收缩预投射代数

Auslander-Reiten's Cohen-Macaulay algebras and contracted preprojective algebras

本文通过证明所有Dynkin类型的收缩预投射代数均为Cohen-Macaulay代数，给出了首个非平凡的Cohen-Macaulay代数类，并否定了Auslander-Reiten关于CM模范畴与$d$次合冲范畴是否一致的猜想。

Tilting Cohen-Macaulay representations

This is a survey on recent developments in Cohen-Macaulay representations via tilting and cluster tilting theory. We explain triangle equivalences between the singularity categories of Gorenstein rings and the derived (or cluster) categories of finite dimensional algebras.