Flat quasi-coherent sheaves of finite cotorsion dimension
Algebraic Geometry
2013-12-04 v4
Abstract
Let X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent and n-perfect(not necessarily of finite krull dimension), we prove that every at quasi-coherent sheaf has finite pure injective dimension. Also, we show that there is an equivalence K(PinfX)---> D(FlatX) of homotopy categories, whenever K(PinfX) is the homotopy category of pure injective at quasi-coherent sheaves and D(FlatX) is the pure derived category of at quasi-coherent sheaves.
Keywords
Cite
@article{arxiv.1307.5505,
title = {Flat quasi-coherent sheaves of finite cotorsion dimension},
author = {Esmaeil Hosseini},
journal= {arXiv preprint arXiv:1307.5505},
year = {2013}
}