Mathematics – Commutative Algebra
Scientific paper
2005-06-14
Mathematics
Commutative Algebra
29 pages. The main changes are the addition of Lemma 2.6, needed in the proof of Theorem 2.7, and Remark 5.11, replacing an in
Scientific paper
It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injective modules. Restricted to compact objects, this statement is a reinterpretation of Grothendieck's duality theorem. Using this equivalence it is proved that the (Verdier) quotient of the category of acyclic complexes of projectives by its subcategory of totally acyclic complexes and the corresponding category consisting of injective modules are equivalent. A new characterization is provided for complexes in Auslander categories and in Bass categories of such rings.
Iyengar Srikanth
Krause Henning
No associations
LandOfFree
Acyclicity versus total acyclicity for complexes over noetherian rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Acyclicity versus total acyclicity for complexes over noetherian rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Acyclicity versus total acyclicity for complexes over noetherian rings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-225127