51 citations · 264 across the 70 of their papers we have counts for
10 papers · 1 filter
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.
Auslander-Reiten sequences on schemes
Peter Jorgensen
Let X be a smooth projective scheme of dimension d >= 1 over the field k, and let C be an indecomposable coherent sheaf on X. Then there is an Auslander-Reiten sequence in the cate…
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…
The Auslander-Reiten quiver of a Poincare duality space
Peter Jorgensen
In a previous paper, math.AT/0304079, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincare duality space, each comp…
Auslander-Reiten triangles and quivers over topological spaces
Peter Jorgensen
In this paper, Auslander-Reiten triangles are introduced into algebraic topology, and it is proved that their existence characterizes Poincare duality spaces. Invariants in the for…
A non-commutative BGG correspondence
Peter Jorgensen
A non-commutative version of the Bernstein-Gel'fand-Gel'fand (BGG) correspondence is set up, and a sample application is given to periodic injective resolutions.
Recognizing dualizing complexes
Peter Jorgensen
Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extensio…