Some remarks on Quillen's D\'evissage theorem

TL;DR

This paper offers a new proof of Quillen's Dévissage theorem by leveraging Barwick's theorem of the heart and a specific short exact sequence of dg categories related to nilpotent extensions.

Contribution

It introduces a novel proof approach for Quillen's Dévissage theorem using dg categories and the theorem of the heart, connecting to Auslander-type constructions.

Findings

Provides a different proof of Quillen's Dévissage theorem

Establishes a link between dg categories and nilpotent extensions

Utilizes Barwick's theorem of the heart in the proof

Abstract

In this paper we give a different proof of Quillen's D\'evissage theorem using Barwick's theorem of the heart. The key ingredient is a certain short exact sequence of dg categories, which is closely related with the Auslander-type construction for nilpotent extensions which was used in the papers of Kuznetsov-Lunts \cite{KL15}, Land-Tamme \cite{LT19} and the author \cite{E20}.