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absolutely pure sheaf

Proceedings of the Edinburgh Mathematical Society (1)

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Pure Injective and Absolutely Pure Sheaves
Part of
Edgar Enochs, Sergio Estrada, Sinem Odabaşi
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 3 / August 2016

Published online by Cambridge University Press:

20 November 2015, pp. 623-640
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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.