51 citations · 264 across the 70 of their papers we have counts for
14 papers · 1 filter
-vectors of 2-Calabi--Yau categories and Borel subalgebras of
Peter Jorgensen, Milen Yakimov
We develop a general framework for -vectors of 2-Calabi--Yau categories, which deals with cluster tilting subcategories that are not reachable from each other and contain infini…
Duality for cochain DG algebras
Peter Jorgensen
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module whic…
Homological properties of cochain Differential Graded algebras
Anders J. Frankild, Peter Jorgensen
Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological re…
Covers, preenvelopes, and purity
Henrik Holm, Peter Jorgensen
We show that if a class of modules is closed under pure quotients, then it is precovering if and only if it is covering, and this happens if and only if it is closed under direct s…
Amplitude inequalities for Differential Graded modules
Peter Jorgensen
Differential Graded Algebras can be studied through their Differential Graded modules. Among these, the compact ones attract particular attention. This paper proves that over a sui…
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…
Finite flat and projective dimension
Peter Jorgensen
Over a right-noetherian algebra admitting a dualizing complex, any left-module with finite flat dimension also has finite projective dimension.
Linear free resolutions over non-commutative algebras
Peter Jorgensen
This paper shows among other things that over a non-commutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions.
Ext vanishing and infinite Auslander-Buchsbaum
Peter Jorgensen
A vanishing theorem is proved for Ext groups over non-commutative graded algebras. Along the way, an "infinite" version is proved of the non-commutative Auslander-Buchsbaum theorem…