A Lazard-like theorem for quasi-coherent sheaves

TL;DR

This paper extends classical module theory results to quasi-coherent sheaves on schemes, establishing a Lazard-like theorem for flat sheaves under certain geometric conditions.

Contribution

It proves a Lazard-like theorem for flat quasi-coherent sheaves on quasi-compact, semi-separated schemes with the resolution property, using Drinfeld's almost projective modules.

Findings

Established a Kaplansky-type theorem for quasi-coherent sheaves.

Proved a Lazard-like theorem for flat quasi-coherent sheaves.

Applied the Hill Lemma in the context of sheaf theory.

Abstract

We study filtration of quasi--coherent sheaves. We prove a version of Kaplansky Theorem for quasi--coherent sheaves, by using Drinfeld's notion of almost projective module and the Hill Lemma. We also show a Lazard-like theorem for flat quasi-coherent sheaves for quasi-compact and semi-separated schemes which satisfy the resolution property.