Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new approach to the classification of torsion pairs. In particular, we classify cosilting modules over cluster-tilted algebras of type . We do this by using a geometric model for finite- and infinite-dimensional modules over such algebras.
Torsion pairs and cosilting in type A˜
Laking, Rosanna
2022-01-01
Abstract
Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new approach to the classification of torsion pairs. In particular, we classify cosilting modules over cluster-tilted algebras of type . We do this by using a geometric model for finite- and infinite-dimensional modules over such algebras.
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