Estrada, Sergio and Guil Asensio, Pedro A. and Prest, Mike and Trlifaj, Jan (2009) Model category structures arising from Drinfeld vector bundles. [MIMS Preprint]
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Abstract
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 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology |
| Depositing User: | Professor Mike Prest |
| Date Deposited: | 07 Jul 2009 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1284 |
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