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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Model category structures on chain complexes of sheaves


Author: Mark Hovey
Journal: Trans. Amer. Math. Soc. 353 (2001), 2441-2457
MSC (2000): Primary 18F20, 14F05, 18E15, 18E30, 18G35, 55U35
Published electronically: January 3, 2001
MathSciNet review: 1814077
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Abstract:

The unbounded derived category of a Grothendieck abelian category is the homotopy category of a Quillen model structure on the category of unbounded chain complexes, where the cofibrations are the injections. This folk theorem is apparently due to Joyal, and has been generalized recently by Beke. However, in most cases of interest, such as the category of sheaves on a ringed space or the category of quasi-coherent sheaves on a nice enough scheme, the abelian category in question also has a tensor product. The injective model structure is not well-suited to the tensor product. In this paper, we consider another method for constructing a model structure. We apply it to the category of sheaves on a well-behaved ringed space. The resulting flat model structure is compatible with the tensor product and all homomorphisms of ringed spaces.


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Additional Information

Mark Hovey
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: hovey@member.ams.org

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02721-0
PII: S 0002-9947(01)02721-0
Received by editor(s): February 24, 2000
Published electronically: January 3, 2001
Article copyright: © Copyright 2001 American Mathematical Society