PURE INJECTIVE AND ABSOLUTELY PURE SHEAVES

被引：12
|
作者：
Enochs, Edgar [1 ]
Estrada, Sergio [2 ]
Odabasi, Sinem [2 ]
机构：
[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA
[2] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2016年 / 59卷 / 03期
关键词：
local purity; categorical purity; concentrated scheme; locally finitely presented category; pure injective sheaf; absolutely pure sheaf; QUASI-COHERENT SHEAVES; CATEGORIES; MODULES; COVERS; RINGS;
D O I：
10.1017/S0013091515000462
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：623 / 640
页数：18
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