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Journal of the London Mathematical Society Advance Access originally published online on January 10, 2008
Journal of the London Mathematical Society 2008 77(1):253-269; doi:10.1112/jlms/jdm107
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© 2008 London Mathematical Society

Locally projective monoidal model structure for complexes of quasi-coherent sheaves on P1(k)

E. Enochs

Department of Mathematics
University of Kentucky
Lexington KY 40506-0027
USA
enochs{at}ms.uky.edu

S. Estrada

Departamento de Matemática Aplicada
Universidad de Murcia
Campus del Espinardo
Espinardo (Murcia) 30100
Spain

J. R. García-Rozas

Departamento de Álgebra y A. Matemático
Universidad de Almería
Almería 04071
Spain
jrgrozas{at}ual.es

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.

The authors are partially supported by the DGI MTM2005-03227.

2000 Mathematics Subject Classification 18G25, 18E30 (primary), 16E05, 55N30 (secondary).

Received March 12, 2007; accepted August 16, 2007; published online January 10, 2008.


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