Title: The flat model structure on Ch(O)
Author: James Gillespie
Email: jrg21@psu.edu

Abstract: Let Ch(O) be the category of chain complexes of O-modules on a
topological space T (where O is a sheaf of rings on T ). We put a
Quillen model structure on this category in which the cofibrant objects
are built out of flat modules. More precisely, these are the dg-flat
complexes. Dually, the fibrant objects will be called dg-cotorsion
complexes. We show that this model structure is monoidal, solving the
previous problem of not having any monoidal model structure on Ch(O). As
a corollary, we have a general framework for doing homological algebra
in the category O-MOD of O-modules. I.e., we have a natural way to
define the functors Ext and Tor in O-MOD.