Relations between semidualizing complexes
Abstract
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.
Keywords
Cite
@article{arxiv.0712.3275,
title = {Relations between semidualizing complexes},
author = {Anders J. Frankild and Sean Sather-Wagstaff and Amelia Taylor},
journal= {arXiv preprint arXiv:0712.3275},
year = {2008}
}
Comments
final version, to appear in J. Commutative Algebra, 27 pages, uses XY-pic