Title: Relative homological algebra in the category of quasi-coherent sheaves
Abstract: In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-coherent sheaf over a scheme (X,OX). Indeed we prove something more general. We define what it is understood by the category of quasi-coherent R-modules, where R is a representation by rings of a quiver Q, and we prove the existence of a flat cover and a cotorsion envelope for quasi-coherent R-modules. Then we use the fact that the category of quasi-coherent sheaves on (X,OX) is equivalent to the category of quasi-coherent R-modules for some Q and R to get our result.
Publication Year: 2005
Publication Date: 2005-07-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 104
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot