tCG Torsion Pairs
Daniel Bravo, Carlos E. Parra

TL;DR
This paper characterizes when the t-structure associated with a torsion pair is compactly generated, introduces the concept of tCG torsion pairs, and describes their properties over specific rings.
Contribution
It introduces the concept of tCG torsion pairs, characterizes them in module categories, and describes their structure over Noetherian and von Neumann regular rings.
Findings
tCG torsion pairs are characterized by finitely presented modules.
Every tCG torsion pair is of finite type, but not vice versa.
Explicit descriptions of tCG torsion pairs over certain rings are provided.
Abstract
We investigate conditions for when the -structure of Happel-Reiten-Smal{\o} associated to a torsion pair is a compactly generated -structure. The concept of a CG torsion pair is introduced and for any ring , we prove that is a CG torsion pair in if, and only if, there exists, a set of finitely presented -modules in , such that . We also show that every CG torsion pair is of finite type, and show that the reciprocal is not true. Finally, we give a precise description of the CG torsion pairs over Noetherian rings and von Neumman regular rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
