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Flat covers and cotorsion envelopes of sheaves
Author(s):
Edgar
Enochs;
Luis
Oyonarte
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1285-1292.
MSC (2000):
Primary 16G10, 18F20;
Secondary 18E15
Posted:
October 24, 2001
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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:
10.1090/S0002-9939-01-06190-1
PII:
S 0002-9939(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
Posted:
October 24, 2001
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
2001,
American Mathematical Society
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