Realisation functors in tilting theory

By Chrysostomos Psaroudakis, Jorge Vit'oria. 2015

91 citations recorded by the source corpus.

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an injective cogenerator. For this purpose we develop a theory of (non-compact, or large) tilting and cotilting objects that generalises the preceding notions in the literature. Within the scope of derived Morita theory for rings we show that, under some assumptions, the realisation functor is a derived tensor product. This fact allows us to approach a problem by Rickard on the shape of derived equivalences. Finally, we apply the techniques of this new derived Morita theory to show that a recollement of derived categories is a derived version of a recollement of abelian categories if and only if there are tilting or cotilting t-structures glueing to a tilting or a cotilting t-structure. As a further application, we answer a question by Xi on a standard form for recollements of derived module categories for finite dimensional hereditary algebras.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2ef8171f03b1f20fa5572f7e47118575985ebbf4

Citations in the corpus

• Torsion pairs in silting theory (2016, unknown): “Let the truncation functors of the associated cosilting t-structure Psaroudakis and Vitória 2015, Lemma 4.5(iii)].”