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Adic Foxby Classes

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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 \(F {\otimes }_{R}^{\mathbf {L}} - \) 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.

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Acknowledgments

We are grateful to Srikanth Iyengar, Liran Shaul, Amnon Yekutieli, and the anonymous referee for helpful comments about this work.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC, 29634, USA

    Sean K. Sather-Wagstaff

  2. College of Arts and Sciences, Dakota State University, 820 N Washington Ave., Madison, SD, 57042, USA

    Richard Wicklein

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  1. Sean K. Sather-Wagstaff
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Correspondence to Sean K. Sather-Wagstaff.

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Sean K. Sather-Wagstaff was supported in part by a grant from the NSA. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Sather-Wagstaff, S.K., Wicklein, R. Adic Foxby Classes. Algebr Represent Theor 24, 1155–1189 (2021). https://doi.org/10.1007/s10468-020-09984-8

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