Pure injective and absolutely pure sheaves
Algebraic Geometry
2016-08-11 v3
Abstract
We study two notions of purity in categories of sheaves: the categorical and the geometric. It is shown that pure injective envelopes exist in both cases under very general assumptions on the scheme. Finally we introduce the class of locally absolutely pure (quasi--coherent) sheaves, with respect to the geometrical purity, and characterize locally Noetherian closed subschemes of a projective scheme in terms of the new class.
Keywords
Cite
@article{arxiv.1307.1729,
title = {Pure injective and absolutely pure sheaves},
author = {Edgar Enochs and Sergio Estrada and Sinem Odabaşı},
journal= {arXiv preprint arXiv:1307.1729},
year = {2016}
}
Comments
Updated version. To appear in Proc. Edinburgh Math. Soc