Geodesic
Quasi-coherent sheaves in commutative and non-commutative geometry
Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 535-554

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We give a definition of quasi-coherent modules for any presheaf of sets on the categories of affine commutative and non-commutative schemes. This definition generalizes the usual one. We study the property of a quasi-coherent module to be a sheaf in various topologies. Using presheaves of groupoids, we construct an embedding of commutative geometry in non-commutative geometry. 
@article{IM2_2003_67_3_a5,
     author = {D. O. Orlov},
     title = {Quasi-coherent sheaves in commutative and non-commutative geometry},
     journal = {Izvestiya. Mathematics },
     pages = {535--554},
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     volume = {67},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a5/}
}
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D. O. Orlov. Quasi-coherent sheaves in commutative and non-commutative geometry. Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 535-554. http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a5/