We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D(Mod-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 D(Mod-A). This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.
PARAMETRIZING TORSION PAIRS IN DERIVED CATEGORIES
Angeleri, Lidia.;
2021-01-01
Abstract
We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D(Mod-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 D(Mod-A). This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.
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