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Pure Injective and Absolutely Pure Sheaves

Published online by Cambridge University Press:  20 November 2015

Edgar Enochs
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA ([email protected])
Sergio Estrada
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain ([email protected]; [email protected])
Sinem Odabaşi
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain ([email protected]; [email protected])

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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