The flat model structure on
Author:
James Gillespie
Translated by:
Journal:
Trans. Amer. Math. Soc. 356 (2004), 33693390
MSC (2000):
Primary 55U35, 18G35, 18G15
Published electronically:
January 29, 2004
MathSciNet review:
2052954
Fulltext PDF Free Access
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Abstract: Given a cotorsion pair in an abelian category with enough objects and enough objects, we define two cotorsion pairs in the category of unbounded chain complexes. We see that these two cotorsion pairs are related in a nice way when is hereditary. We then show that both of these induced cotorsion pairs are complete when is the ``flat'' cotorsion pair of modules. This proves the flat cover conjecture for (possibly unbounded) chain complexes and also gives us a new ``flat'' model category structure on . In the last section we use the theory of model categories to show that we can define using a flat resolution of and a cotorsion coresolution of .
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 E. Enochs, S. Estrada, J.R. GarcíaRozas, and L. Oyonarte, Flat covers of quasicoherent sheaves, preprint, 2000.
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 Pierre Antoine Grillet, Algebra, Pure and Applied Mathematics, John Wiley & Sons, New York, 1999. MR 2000g:20001
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Additional Information
James Gillespie
Affiliation:
Department of Mathematics, 4000 University Drive, Penn State–McKeesport, McKeesport, Pennsylvania 151327698
Email:
jrg21@psu.edu
DOI:
http://dx.doi.org/10.1090/S0002994704034166
PII:
S 00029947(04)034166
Received by editor(s):
October 1, 2002
Received by editor(s) in revised form:
May 13, 2003
Published electronically:
January 29, 2004
Additional Notes:
The author thanks Mark Hovey of Wesleyan University
Article copyright:
© Copyright 2004 American Mathematical Society
