Parametrizing torsion pairs in derived categories

Angeleri Hügel, Lidia; Hrbek, Michal

doi:10.1090/ert/579

Parametrizing torsion pairs in derived categories
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by Lidia Angeleri Hügel and Michal Hrbek

Represent. Theory 25 (2021), 679-731

DOI: https://doi.org/10.1090/ert/579

Published electronically: July 30, 2021

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Abstract:

We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category $\mathrm {D}({\mathrm {Mod}}\text {-}A)$ of a ring $A$. To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in $A$, which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in $\mathrm {D}({\mathrm {Mod}}\text {-}A)$. This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.

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