Flat covers and cotorsion envelopes of sheaves

Authors:
Edgar Enochs and Luis Oyonarte

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1285-1292

MSC (2000):
Primary 16G10, 18F20; Secondary 18E15

DOI:
https://doi.org/10.1090/S0002-9939-01-06190-1

Published electronically:
October 24, 2001

MathSciNet review:
1879949

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove that any sheaf of modules over any topological space (in fact, any -module where is a sheaf of rings on the topological space) has a flat cover and a cotorsion envelope. This result is very useful, as we shall explain later in the introduction, in order to compute cohomology, due to the fact that the category of sheaves ( -modules) does not have in general enough projectives.

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Additional Information

**Edgar Enochs**

Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Email:
enochs@ms.uky.edu

**Luis Oyonarte**

Affiliation:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04071 Almería, Spain

Email:
oyonarte@ual.es

DOI:
https://doi.org/10.1090/S0002-9939-01-06190-1

Keywords:
Flat (pre)cover,
cotorsion (pre)envelope,
(pre)sheaf,
$\mathcal{O}$-(pre)module,
Grothendieck category

Received by editor(s):
July 26, 2000

Received by editor(s) in revised form:
November 3, 2000

Published electronically:
October 24, 2001

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 2001
American Mathematical Society