7 papers · 1 filter
Finite Cohen-Macaulay type and smooth non-commutative schemes
Peter Jorgensen
A commutative local Cohen-Macaulay ring R of finite Cohen-Macaulay type is known to be an isolated singularity; that is, Spec(R)-m is smooth. This paper proves a non-commutative an…
Existence of Gorenstein projective resolutions
Peter Jorgensen
Gorenstein rings are important to mathematical areas as diverse as algebraic geometry, where they encode information about singularities of spaces, and homotopy theory, through the…
Symmetry theorems for Ext vanishing
Peter Jorgensen
It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vani…
Tate cohomology over fairly general rings
Peter Jorgensen
Tate cohomology was originally defined over finite groups. More recently, Avramov and Martsinkovsky showed how to extend the definition so that it now works well over Gorenstein ri…
The Gorenstein projective modules are precovering
Peter Jorgensen
The Gorenstein projective modules are proved to form a precovering class in the module category of a ring which has a dualizing complex.
The homotopy category of complexes of projective modules
Peter Jorgensen
The homotopy category of complexes of projective left-modules over any reasonably nice ring is proved to be a compactly generated triangulated category, and a duality is given betw…