  We will generalize the projective model structure in the category of
unbounded complexes of modules over a commutative ring to the category of
unbounded complexes of quasi-coherent sheaves over the projective line.
Concretely we will define a locally projective model structure in the category
of complexes of quasi-coherent sheaves on the projective line. In this model
structure the cofibrant objects are the dg-locally projective complexes. We
also describe the fibrations of this model structure and show that the model
structure is monoidal. We point out that this model structure is necessarily
different from other known model structures such as the injective model
structure and the locally free model structure.
