## 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)

Zbl 0182.260
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### References:

 [1] Adams, J.F.: Stable Homotopy and Generalized Homology. Chicago: University of Chicago Press 1974 · Zbl 0309.55016 [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 [3] Artin, M., Mazur, B.: Etale Homotopy. Lecture notes in Math. 100. Berlin: Springer-Verlag 1969 · Zbl 0182.26001 [4] Atiyah, M., Hirzebruch, F.: Vector bundles and homogeneous spaces. Proc. of Sym. in Pure Math.III, 7-38 (1961) · Zbl 0108.17705 [5] Bass, H.: AlgebraicK-theory. New York: Benjamin 1968 · Zbl 0174.30302 [6] Boardman, J.M.: Stable Homotopy Theory. University of Warwick Notes [7] Browder, W.: AlgebraicK-theory with coefficients ?/p. Lecture notes in Math. 651 pp. 40-84. Berlin: Springer-Verlag 1978 [8] Deligne, P.: Cohomologie Etale (SGA 41/2). Lecture notes in Math. 569. Berlin: Springer-Verlag 1977 [9] Friedlander, E.: Fibrations in etale homotopy theory. Publ. Math. I.H.E.S.42, 5-46 (1972) · Zbl 0351.55011 [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 [16] Sullivan, D.: Genetics of homotopy theory and the Adams conjecture. Annals of Math.100, 1-79 (1974) · Zbl 0355.57007 [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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