Pure injective and absolutely pure sheaves

2013/07/05 by Enochs, Edgar, Estrada, Sergio, Odabaşı, Sinem
#14A15 #16D90 #18C35 #18D10 #18E15 #18F20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.1729

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.

Related

• Purity in categories of sheaves
• The Pure derived category of quasi-coherent sheaves
• Purity and decomposition theorems for staggered sheaves
• Flat quasi-coherent sheaves of finite cotorsion dimension
• Locally finitely presented categories with no flat objects