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.
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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/

[1] Artin M., Grothendieck A., Verdier J. L., “Théorie des Topos et Cohomologie Etale des Schémas”, SGA4, Lecture Notes in Math., 269, Springer, Heidelberg, 1972 | MR

[2] Berthelot P., Grothendieck A., Illusie L., “Théorie des intersections et théoreme de Riemann-Roch”, SGA6, Lect. Notes in Math., 225, Springer, Heidelberg, 1971 | MR | Zbl

[3] Grothendieck A., “Revetements étale et groups fondamental”, SGA1, Lecture Notes in Math., 224, Springer, Heidelberg, 1971 | MR

[4] Faith C., Algebra: Rings, Modules and Categories, V. I, Springer, Berlin–Heidelberg–N. Y., 1973 | MR | Zbl

[5] Mac Lane S., Moerdijk I., Sheaves in Geometry and Logic, Springer, Berlin–Heidelberg–N. Y., 1992

[6] Knus M. A., Ojanguren M., Théorie de la Descente et Algèbres d'Azumaya, Lect. Notes in Math., 389, Springer, Heidelberg, 1974 | MR | Zbl

[7] Murre J., Lectures on an Introduction to Grothendieck's Theory of the Fundamental Group, Lect. Notes, 40, Tata Institute of Fundamental Research, Bombay, 1967 | MR