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Weakly Stable Torsion Classes

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Abstract

Weakly stable torsion classes were introduced by the author and Yekutieli to provide a torsion theoretic characterisation of the notion of weak proregularity from commutative algebra. In this paper we investigate weakly stable torsion classes, with a focus on aspects related to localisation and completion. We characterise when torsion classes arising from left denominator sets and idempotent ideals are weakly stable. We show that every weakly stable torsion class T can be associated with a dg ring AT; in well behaved situations there is a homological epimorphism A → AT. We end by studying torsion and completion with respect to a single regular and normal element.

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Acknowledgments

The author would like to thank Amnon Yekutieli for his assistance and many suggestions regarding the material in this paper, and the anonymous referee for their comments.

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Author notes

  1. Rishi Vyas

    Present address: , Delhi, India

Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University, Be’er Sheva, 84105, Israel

    Rishi Vyas

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  1. Rishi Vyas
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Correspondence to Rishi Vyas.

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Presented by: Jan Stovicek

This work was completed when the author was supported by: Israel Science Foundation grants 253/13 and 170/12, the Center for Advanced Studies in Mathematics at Ben-Gurion University of the Negev, and the Israel Council for Higher Education.

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Vyas, R. Weakly Stable Torsion Classes. Algebr Represent Theor 22, 1183–1207 (2019). https://doi.org/10.1007/s10468-018-9817-1

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  • DOI: https://doi.org/10.1007/s10468-018-9817-1

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