2007/12/19 by Anders J. Frankild, Anders Frankild, Sean Sather-Wagstaff +4
Mathematics · #13D05 #13D07 #13D25 #13H10 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D05 #msc:13D07 #msc:13D25 #msc:13H10
paper · pdf · doi:10.48550/arxiv.0712.3275
final version, to appear in J. Commutative Algebra, 27 pages, uses XY-pic
openalex publication_date 2007/12/19 · arxiv created 2008/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the following question: Given two semidualizing complexes B and C over a commutative noetherian ring R, does the vanishing of ExtnR(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 ExtnR(B,C)=0 for all n>>0. We introduce and investigate an equivalence relation ≈ 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 ExtnR(B,C)=0 for all n>>0. Finally, we answer our original question in some special cases.