On a property of t-structures generated by non-classical tilting modules

2016/03/31 by Francesco Mattiello, Mattiello, Francesco
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1603.09503

openalex publication_date 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a ring and T ∈ \rm Mod-R be a (non-classical) tilting module of finite projective dimension. Let \mathcal T=(\mathcal T^≤0, \mathcal T^≥0) be the t-structure on D(R) generated by T and \mathcal D=(\mathcal D^≤0, \mathcal D^≥0) be the natural t-structure. We show that the pair (\mathcal D, \mathcal T) is right filterable in the sense of [FMT14], that is, for any i∈\mathbb Z the intersection \mathcal D^{≥ i}∩ \mathcal T^{≥ 0} is the co-aisle of a t-structure. As a consequence, the heart of \mathcal T is derived equivalent to \rm Mod-R.

Related

• Pure Projective Tilting Modules
• Lifting and restricting t-structures
• Tilting theory for extended module categories
• Topological endomorphism rings of tilting complexes
• Tilting modules arising from ring epimorphisms