Torsion pairs were introduced by Dickson in 1966 as a generalization of the concept of torsion
abelian group to arbitrary abelian categories. Using torsion pairs, we can divide complex abelian
categories in smaller parts which are easier to understand.
In this thesis we discuss torsion pairs in the category of modules over a finite-dimensional algebra, in
particular we explore the relation between torsion pairs in the category of all modules and torsion
pairs in the category of finite-dimensional modules.
In the second chapter of the thesis, we present the analogue of a classical theorem of Auslander in the
context of τ-tilting theory: for a finite-dimensional algebra the number of torsion pairs in the
category of finite-dimensional modules is finite if and only if every brick over such algebra is finite-
dimensional.
In the third chapter, we revisit the Ingalls-Thomas correspondences between torsion pairs and wide
subcategories in the context of large torsion pairs. We provide a nice description of the resulting
wide subcategories and show that all such subcategories are coreflective.
In the final chapter, we describe mutation of cosilting modules in terms of an operation on the Ziegler
spectrum of the algebra.
| Identifer | oai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/348239 |
| Date | 30 June 2022 |
| Creators | Sentieri, Francesco |
| Contributors | Sentieri, Francesco |
| Publisher | Università degli studi di Trento, place:TRENTO |
| Source Sets | Università di Trento |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | firstpage:1, lastpage:101, numberofpages:101 |
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