Torsion pairs and filtrations in abelian categories with tilting objects

2013/02/13 by Lo, Jason
#18E30 (Primary) 14F05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1302.2991

Abstract

Given a noetherian abelian category \mathcal Z of homological dimension two with a tilting object T, the abelian category \mathcal Z and the abelian category of modules over End (T)^op are related by a sequence of two tilts; we give an explicit description of the torsion pairs involved. We then use our techniques to obtain a simplified proof of a theorem of Jensen-Madsen-Su, that \mathcal Z has a three-step filtration by extension-closed subcategories. Finally, we generalise Jensen-Madsen-Su's filtration to a noetherian abelian category of any finite homological dimension.

Related

• Filtrations in abelian categories with a tilting object of homological dimension two
• Filtrations of torsion classes in proper abelian subcategories
• Intervals of torsion pairs and generalized Happel-Reiten-Smalø tilting
• Tilting theory for extended module categories
• N-Quasi-Abelian Categories vs N-Tilting Torsion Pairs