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2009.43: Model category structures arising from Drinfeld vector bundles

2009.43: Sergio Estrada, Pedro A. Guil Asensio, Mike Prest and Jan Trlifaj (2009) Model category structures arising from Drinfeld vector bundles.

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We present a general construction of model category structures on the category $\Ch(\Qco(X))$ of unbounded chain complexes of quasi-coherent sheaves on a semi-separated scheme $X$. The construction is based on making compatible the filtrations of individual modules of sections at open affine subsets of $X$. It does not require closure under direct limits as previous methods. We apply it to describe the derived category $\mathbb D (\Qco(X))$ via various model structures on $\Ch(\Qco(X))$. As particular instances, we recover recent results on the flat model structure for quasi-coherent sheaves. Our approach also includes the case of (infinite-dimensional) vector bundles, and of restricted flat Mittag-Leffler quasi-coherent sheaves, as introduced by Drinfeld. Finally, we prove that the unrestricted case does not induce a model category structure as above in general.

Item Type:MIMS Preprint
Uncontrolled Keywords:Drinfeld vector bundle, model category structure, flat Mittag-Leffler module
Subjects:MSC 2000 > 14 Algebraic geometry
MSC 2000 > 18 Category theory; homological algebra
MSC 2000 > 55 Algebraic topology
MIMS number:2009.43
Deposited By:Professor Mike Prest
Deposited On:07 July 2009

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