Adic Foxby Classes

2016/02/10 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Richard Wicklein +1 · 3 citations
Mathematics · #13B35 #13C12 #13D09 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13B35 #msc:13C12 #msc:13D09 #msc:13D45

paper · pdf · doi:10.48550/arxiv.1602.03227

32 pages. part 6 of a series with arXiv:1401.6925, arXiv:1506.07052, arXiv:1602.03224, arXiv:1602.03225, and arXiv:1602.03226. comments welcome. v.2 has updated references and updated URL for Sather-Wagstaff

arxiv created 2016/02/23 · arxiv updated 2016/02/25

Abstract

We continue our work on adic semidualizing complexes over a commutative noetherian ring R by investigating the associated Auslander and Bass classes (collectively known as Foxby classes), following Foxby and Christensen. Fundamental properties of these classes include Foxby Equivalence, which provides an equivalence between the Auslander and Bass classes associated to a given adic semidualizing complex. We prove a variety of stability results for these classes, for instance, with respect to F⊗^L_R- where F is an R-complex finite flat dimension, including special converses of these results. We also investigate change of rings and local-global properties of these classes.

Citations

• Support and adic finiteness for complexes
• Adic semidualizing complexes
• Adically Finite Chain Complexes
• Adic Finiteness: Bounding Homology and Applications
• Extended Local Cohomology and Local Homology

Cited by

• Adic semidualizing complexes
• Adically Finite Chain Complexes
• Adic Finiteness: Bounding Homology and Applications
• Extended Local Cohomology and Local Homology

Related

• Foxby equivalence over associative rings
• Adic semidualizing complexes
• On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence
• Foxby equivalence relative to C-weak injective and C-weak flat modules
• Cartan-Eilenberg complexes and Auslander categories