The Derived Category of quasi-coherent sheaves on an Artin stack via model structures

TL;DR

This paper introduces a new approach to defining the derived category of quasi-coherent sheaves on Artin stacks using Quillen model structures, providing a homotopical framework for such categories.

Contribution

It constructs two Quillen monoidal model structures on complexes of quasi-coherent modules to define the derived category for Artin stacks, advancing the homotopical understanding.

Findings

Establishment of two Quillen monoidal model structures

Homotopy category equivalence with derived category of quasi-coherent sheaves

Framework applicable to unbounded complexes on Artin stacks

Abstract

We define the derived category of quasi--coherent modules for certain Artin stacks as the homotopy category of two Quillen monoidal model structures on the corresponding category of unbounded complexes of quasi--coherent modules.