Recollements from partial tilting complexes

TL;DR

This paper generalizes Rickard's Theorem by exploring recollements of derived categories of dg-algebras induced by self-orthogonal objects, extending known results for partial tilting modules and connecting to universal localizations.

Contribution

It introduces a broad framework for recollements from partial tilting complexes, extending existing triangle equivalences and linking to universal localizations.

Findings

Generalization of Rickard's Theorem for dg-algebras

Extension of triangle equivalences for partial tilting modules

Connection established between recollements, bireflective subcategories, and universal localizations

Abstract

We consider recollements of derived categories of dg-algebras induced by self orthogonal compact objects obtaining a generalization of Rickard's Theorem. Specializing to the case of partial tilting modules over a ring, we extend the results on triangle equivalences proved in [B2] and [BMT]. In the end we focus on the connection between recollements of derived categories of rings, bireflective subcategories and generalized universal localizations".