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2021 Definable coaisles over rings of weak global dimension at most one
Silvana Bazzoni, Michal Hrbek
Publ. Mat. 65(1): 165-241 (2021). DOI: 10.5565/PUBLMAT6512106

Abstract

In the setting of the unbounded derived category $\mathbf{D}(R)$ of a ring $R$ of weak global dimension at most one we consider t-structures with a definable coaisle. The t-structures among these which are stable (that is, the t-structures which consist of a pair of triangulated subcategories) are precisely the ones associated to a smashing localization of the derived category. In this way, our present results generalize those of [8] to the non-stable case. As in the stable case [8], we confine for the most part to the commutative setting, and give a full classification of definable coaisles in the local case, that is, over valuation domains. It turns out that, unlike in the stable case of smashing subcategories, the definable coaisles do not always arise from homological ring epimorphisms. We also consider a non-stable version of the Telescope Conjecture for t-structures and give a ring-theoretic characterization of the commutative rings of weak global dimension at most one for which it is satisfied.

Funding Statement

The first named author was partially supported by grants BIRD163492 and DOR1690814 of Padova University. The second named author was partially supported by the Czech Academy of Sciences Programme for research and mobility support of starting researchers, project MSM100191801.

Citation

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Silvana Bazzoni. Michal Hrbek. "Definable coaisles over rings of weak global dimension at most one." Publ. Mat. 65 (1) 165 - 241, 2021. https://doi.org/10.5565/PUBLMAT6512106

Information

Received: 5 September 2019; Revised: 30 July 2020; Published: 2021
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185831
Digital Object Identifier: 10.5565/PUBLMAT6512106

Subjects:
Primary: 13C05 , 13D09
Secondary: 18A20 , 18E30

Keywords: cosilting complex , derived category , homological epimorphism , telescope conjecture , t-structure

Rights: Copyright © 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.65 • No. 1 • 2021
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