Relative homological algebra in the category of quasi-coherent sheaves |
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Authors: | Edgar Enochs |
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Institution: | a Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA b Departamento de Álgebra, Universidad de Granada, 51002 Ceuta, Spain |
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Abstract: | In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-coherent sheaf over a scheme (X,OX). Indeed we prove something more general. We define what it is understood by the category of quasi-coherent R-modules, where R is a representation by rings of a quiver Q, and we prove the existence of a flat cover and a cotorsion envelope for quasi-coherent R-modules. Then we use the fact that the category of quasi-coherent sheaves on (X,OX) is equivalent to the category of quasi-coherent R-modules for some Q and R to get our result. |
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Keywords: | Primary 16D90 Secondary 18F20 |
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