Geodesic
Homotopic properties of algebraic vector bundles
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 261-263 
A. L. Smirnov. Homotopic properties of algebraic vector bundles. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 261-263. http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a8/
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     author = {A. L. Smirnov},
     title = {Homotopic properties of algebraic vector bundles},
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     year = {2004},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A technique is given which allows to work easily with vector bundles in homotopic algebraic geometry just as in topology. In particular it is proven that any monomorphism and any epimorphism of algebraic vector bundles can be split homotopically and that the tautological vector bundle on the Grassmanian is homotopically universal.

[1] I. Panin, A. Smirnov, Push-forwards in oriented cohomology theories of algebraic varieties, K-theory Preprint Archives, 459, 2000

[2] F. Morel, V. Voevodsky, Homotopy category of schemes over a base, Preprint, 1997

[3] V. Voevodsky, “$\mathbb{A}^1$-Homotopy theory”, Proceedings of the International Congress of Mathematicians, Vol. I, Berlin, 1998, Doc. Math., 1 (1998), 417–442, Extra Vol. ICM | MR

[4] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl