Adic Foxby Classes
Abstract
We continue our work on adic semidualizing complexes over a commutative noetherian ring 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 where is an -complex finite flat dimension, including special converses of these results. We also investigate change of rings and local-global properties of these classes.
Cite
@article{arxiv.1602.03227,
title = {Adic Foxby Classes},
author = {Sean Sather-Wagstaff and Richard Wicklein},
journal= {arXiv preprint arXiv:1602.03227},
year = {2016}
}
Comments
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