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Etale K-theory. I: Connections with etale cohomology and algebraic vector bundles. (English) Zbl 0519.14010

MSC:
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14C99 Cycles and subschemes
14F35 Homotopy theory and fundamental groups in algebraic geometry
55N15 Topological \(K\)-theory
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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References:
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[2] Araki, S., Toda, H.: Multiplicative structures in modq cohomology theories, I and II, Osaka J. Math.2, 71-115 (1965) and3, 81-120 (1966) · Zbl 0129.15201
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[10] Friedlander, E.: Etale Homotopy of Simplicial Schemes. to appear · Zbl 0538.55001
[11] Friedlander, E.: EtaleK-theory II: Connections with algebraicK-theory. to appear
[12] Grothendieck, A.: La theorie des classes de Chern. Bull. Soc. Math. France vol86, 137-154 (1958) · Zbl 0091.33201
[13] Jouanolou, J.-P.: Une suite’ exacte de Mayer-Vietoris enK-theorie algebraique. Lecture notes in Math. 341, pp. 293-316. Berlin: Springer-Verlag 1973
[14] Kleiman, S.: Geometry on grassmannians and applications to splitting bundles and smoothing cycles, Pub. I.H.E.S.36, 281-298 (1969) · Zbl 0208.48501
[15] Quillen, D.: Some remarks on etale homotopy and a conjecture of Adams, Topology7, 111-116 (1968) · Zbl 0157.30303 · doi:10.1016/0040-9383(68)90017-7
[16] Sullivan, D.: Genetics of homotopy theory and the Adams conjecture. Annals of Math.100, 1-79 (1974) · Zbl 0355.57007 · doi:10.2307/1970841
[17] Tate, J.: Algebraic cycles and poles of zeta functions. In: Arithmetic Algebraic Geometry, pp. 93-110. New York: Harper & Row 1965 · Zbl 0213.22804
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