The projective stable category of a coherent scheme

TL;DR

This paper introduces the projective stable category for coherent schemes, establishing a new homotopy category framework based on an abelian model structure on chain complexes of quasi-coherent sheaves.

Contribution

It defines the projective stable category for coherent schemes and characterizes cofibrant objects as complexes of flat quasi-coherent sheaves with a specific acyclicity property.

Findings

Established the homotopy category of the model structure.

Characterized cofibrant objects as special complexes of flat sheaves.

Provided foundational framework for further homological algebra in schemes.

Abstract

We define the projective stable category of a coherent scheme. It is the homotopy category of an abelian model structure on the category of unbounded chain complexes of quasi-coherent sheaves. We study the cofibrant objects of this model structure, which are certain complexes of flat quasi-coherent sheaves satisfying a special acyclicity condition.