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Friedlander, Eric M.

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

Invent. Math. 60, 105-134 (1980).
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Cited in 3 Reviews
Cited in 15 Documents

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)

Keywords:

topological K-theory; algebraic K-theory; etale K-theory; etale homotpy; etale cohomology; l-adic cohomology; algebraic cycles; Tate conjecture on algebraic cycles

Citations:

Zbl 0182.260
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\textit{E. M. Friedlander}, Invent. Math. 60, 105--134 (1980; Zbl 0519.14010)
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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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