Derived equivalences of upper-triangular ring spectra via lax limits

TL;DR

This paper generalizes existing theorems on derived equivalences of upper-triangular matrix rings from ordinary rings to the setting of ring spectra, broadening the scope of such equivalences.

Contribution

It extends Ladkani's theorem and Maycock's differential graded algebra theorem to the context of ring spectra, providing a new framework for derived equivalences.

Findings

Generalization of Ladkani's theorem to ring spectra

Extension of Maycock's theorem for differential graded algebras

Broader applicability of derived equivalence results

Abstract

We extend a theorem of Ladkani concerning derived equivalences between upper-triangular matrix rings from ordinary rings to ring spectra. Our result also extends an analogous theorem of Maycock for differential graded algebras.