Orlov's equivalence and maximal Cohen-Macaulay modules over the cone of an elliptic curve

Maximal Cohen-macaulay Modules over Hypersurface Rings

This paper is a brief survey on various methods to classify maximal Cohen-Macaulay modules over hypersurface rings. The survey focuses on the contributions in this topic of Dorin Popescu together with his collaborators.

Rank One Maximal Cohen-macaulay Modules Over

Maximal Cohen-Macaulay Modules over the Affine Cone of the Simple Node

A concrete description of all graded maximal Cohen–Macaulay modules of rank one and two over the non-isolated singularities of type y3 1 +y 2 1y3−y 2y3 is given. For this purpose we construct an alghoritm that provides extensions of MCM modules over an arbitrary hypersurface.

Cohen-macaulay Modules and Holonomic Modules over Filtered Rings

We study Gorenstein dimension and grade of a module M over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G-dimM ≤ G-dimgrM and an equality gradeM = grade grM , whe...

ON THE EXISTENCE OF MAXIMAL COHEN-MACAULAY MODULES OVER p th ROOT EXTENSIONS

Let S be an unramified regular local ring having mixed characteristic p > 0 and R the integral closure of S in a pth root extension of its quotient field. We show that R admits a finite, birational module M such that depth(M) = dim(R). In other words, R admits a maximal Cohen-Macaulay module.