Relations between semidualizing complexes
| dc.creator | Frankild, Anders J. | |
| dc.creator | Sather-Wagstaff, Sean | |
| dc.creator | Taylor, Amelia | |
| dc.date | 2007-12-19 | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T09:25:06Z | |
| dc.date.available | 2026-07-07T09:25:06Z | |
| dc.description | We study the following question: Given two semidualizing complexes B and C over a commutative noetherian ring R, does the vanishing of Ext^n_R(B,C) for n>>0 imply that B is C-reflexive? This question is a natural generalization of one studied by Avramov, Buchweitz, and Sega. We begin by providing conditions equivalent to B being C-reflexive, each of which is slightly stronger than the condition Ext^n_R(B,C)=0 for all n>>0. We introduce and investigate an equivalence relation \approx on the set of isomorphism classes of semidualizing complexes. This relation is defined in terms of a natural action of the derived Picard group and is well-suited for the study of semidualizing complexes over nonlocal rings. We identify numerous alternate characterizations of this relation, each of which includes the condition Ext^n_R(B,C)=0 for all n>>0. Finally, we answer our original question in some special cases. | |
| dc.description | final version, to appear in J. Commutative Algebra, 27 pages, uses XY-pic | |
| dc.identifier | https://arxiv.org/abs/0712.3275 | |
| dc.identifier | http://arxiv.org/abs/0712.3275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156296 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D05, 13D07, 13D25, 13H10 | |
| dc.title | Relations between semidualizing complexes | |
| dc.type | text |