2,278 research outputs found
Pure injective and absolutely pure sheaves
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.Comment: Updated version. To appear in Proc. Edinburgh Math. So
- …