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Parametrizing torsion pairs in derived categories


Authors: Lidia Angeleri Hügel and Michal Hrbek
Journal: Represent. Theory 25 (2021), 679-731
MSC (2020): Primary 18G80, 18E40, 16S85; Secondary 16E60, 16G20, 13C05
DOI: https://doi.org/10.1090/ert/579
Published electronically: July 30, 2021
MathSciNet review: 4293772
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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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Additional Information

Lidia Angeleri Hügel
Affiliation: Dipartimento di Informatica - Settore di Matematica, Università degli Studi di Verona, Strada le Grazie 15 - Ca’ Vignal, I-37134 Verona, Italy
MR Author ID: 358523
ORCID: 0000-0002-9283-1260
Email: lidia.angeleri@univr.it

Michal Hrbek
Affiliation: Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Prague, Czech Republic
MR Author ID: 1048669
ORCID: 0000-0001-7457-5112
Email: hrbek@math.cas.cz

Received by editor(s): June 26, 2020
Received by editor(s) in revised form: January 15, 2021
Published electronically: July 30, 2021
Additional Notes: The first author was partially supported by Istituto Nazionale di Alta Matematica INdAM-GNSAGA. The second author was supported by the Czech Academy of Sciences Programme for research and mobility support of starting researchers, project MSM100191801
Article copyright: © Copyright 2021 American Mathematical Society