Algebraic $K$-theory and etale cohomology

Thomason, R. W.

doi:10.24033/asens.1495

Algebraic

K

-theory and etale cohomology

Thomason, R. W.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 3, pp. 437-552

corrigé par Erratum “Algebraic

K

-theory and etale cohomology”

MR Zbl | 10 citations dans Numdam

DOI : 10.24033/asens.1495

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     title = {Algebraic $K$-theory and etale cohomology},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {437--552},
     year = {1985},
     publisher = {Elsevier},
     volume = {Ser. 4, 18},
     number = {3},
     doi = {10.24033/asens.1495},
     mrnumber = {87k:14016},
     zbl = {0596.14012},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.1495/}
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Thomason, R. W. Algebraic $K$-theory and etale cohomology. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 3, pp. 437-552. doi: 10.24033/asens.1495

Bibliographie
Cité par

[1] J. F. Adams, Stable Homotopy and Generalized Homology, Univ. of Chicago Press, 1974. | Zbl | MR

[2] S. Araki and H. Toda, Multiplicative Structures in mod q Cohomology Theories, I and II (Osaka J. Math., Vol. 2, 1965, pp. 71-115 ; Vol. 3, 1966, pp. 80-120). | Zbl | MR

[3] M. Artin, Grothendieck Topologies (Lecture Notes, Harvard Univ., 1962). | Zbl

[4] M. Artin, On the Joins of Hensel Rings (Advances in Math., Vol. 7, 1971, pp. 282-296). | Zbl | MR

[5] M. Artin and B. Mazur, Etale Homotopy (Springer Lecture Notes in Math., Vol. 100, 1969). | Zbl | MR

[6] M. Artin and J.-L. Verdier, Seminar on Etale Cohomology of Number Fields (Summer Institute on Algebraic Geometry, Woods Hole, 1964, mineographed notes).

[7] M. Barr, Toposes without Points (J. Pure Appl. Alg., Vol. 5, 1974, pp. 265-280). | Zbl | MR

[8] A. A. Beilinson, Higher Regulators and Values of L-Functions of Curves (Funct. Anal. and Appl., Vol. 14, No. 2, 1980, pp. 116-118). | Zbl | MR

[9] A. A. Beilinson, Visshi regulyatori i znacheniya L-funcni, (Sovremennge Problemy Matematiki, Vol. 24, 1984, pp. 181-238). | MR

[10] J. M. Boardman, Conditionally Convergent Spectral Sequences, preprint, 1981. | MR

[11] A. K. Bousfield, The Localization of Spaces with Respect to Homology (Topology, Vol. 14, 1975, pp. 133-150). | Zbl | MR

[12] A. K. Bousfield, The Localization of Spectra with Respect to Homology (Topology, Vol. 18, 1979, pp. 257-281). | Zbl | MR

[13] A. K. Bousfield, K-Localizations and K-Equivalences of Infinite Loop Spaces (Proc. London Math. Soc., Ser. 3, Vol. 44, 1982, pp. 291-311). | Zbl | MR

[14] A. K. Bousfield and E. M. Friedlander, Homotopy Theory of Г-Spaces, Spectra, and Bisimplicial Sets (Geometric Applications of Homotopy Theory II, Springer Lecture Notes in Math., Vol. 658, 1978, pp. 80-130). | Zbl | MR

[15] A. K. Bousfield and D. M. Kan, The Homotopy Spectral Sequence of a Space with Coefficients in a Ring (Topology, Vol. 11, 1972, pp. 79-106). | Zbl | MR

[16] A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions, and Localizations (Springer Lecture Notes in Math., Vol. 304, 1972). | Zbl | MR

[17] W. Browder, Algebraic K-Theory with Coefficients ℤ/p (Geometric Applications of Homotopy Theory I, Springer Lecture Notes in Math., Vol. 657, pp. 40-84). | Zbl | MR

[18] K. S. Brown, Abstract Homotopy Theory and Generalized Sheaf Cohomology (Trans. Amer. Math. Soc., Vol. 186, 1973, pp. 419-458). | Zbl | MR

[19] K. S. Brown, Cohomology of Groups (Graduate Texts in Math., Vol. 87, Springer, 1982). | Zbl | MR

[20] K. S. Brown and S. M. Gersten, Algebraic K-Theory as Generalized Sheaf Cohomology (Higher K-Theories, Springer Lecture Notes in Math., Vol. 341, 1973, pp. 266-292). | Zbl | MR

[21] H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, 1956. | Zbl | MR

[22] E. B. Curtis, Simplicial Homotopy Theory (Advances in Math., Vol. 6, 1971, pp. 107-209). | Zbl | MR

[23] B. H. Dayton and C. A. Weibel, A Spectral Sequence for the K-Theory of Affine Glued Schemes, (Algebraic K-Theory : Evanston 1980, Springer Lecture Notes in Math., Vol. 854, 1981, pp. 24-92). | Zbl | MR

[24] P. Deligne, Théorie de Hodge III (Publ. Math. I.H.E.S., Vol. 44, 1974, pp. 5-77). | Zbl | MR | Numdam

[25] T. Tom Dieck, Transformation Groups and Representation Theory (Springer Lecture Notes in Math., Vol. 766, 1979). | Zbl | MR

[26] A. Dold, Homology of Symmetric Products and Other Functors of Complexes (Ann. Math., Vol. 68, 1958, pp. 54-80). | Zbl | MR

[27] A. Dold and D. Puppe, Homologie Nich-Additive-Funktoren. Anwendungen (Ann. Inst. Fourier, Vol. 11, 1961, pp. 201-312). | Zbl | MR | Numdam

[28] A. Dress, Contributions to the Theory of Induced Representations (Classical Algebraic K-theory, and Connections with Arithmetic, Springer Lecture Notes in Math., Vol. 342, 1973, pp. 183-240). | Zbl | MR

[29] E. Dubuc, Kan Extensions in Enriched Category Theory (Springer Lectures Notes in Math., Vol. 145, 1970). | Zbl | MR

[30] W. Dwyer and E. Friedlander, Etale K-Theory and Arithmetic, preprint, 1983. | MR

[31] W. Dwyer, E. Friedlander, V. Snaith and R. Thomason, Algebraic K-Theory Eventually Surjects onto Topological K-Theory (Invent. Math., Vol. 66, 1982, pp. 481-491). | Zbl | MR

[32] E. Dyer, Cohomology Theories, Benjamin, 1969. | Zbl | MR

[33] E. Friedlander, Computations of K-Theories of Finite Fields (Topology, Vol. 15, 1976, pp. 87-109). | Zbl | MR

[34] E. Friedlander, Etale K-Theory I : Connections with Etale Cohomology and Algebraic Vector Bundles (Invent. Math., Vol. 60, 1980, pp. 105-134). | Zbl | MR

[35] E. Friedlander, Etale K-Theory II : Connections with Algebraic K-Theory (Ann. scient. Ec. Norm. Sup., Vol. 15, 1982, pp. 231-256). | Zbl | MR | Numdam

[36] E. Friedlander, Etale Homotopy of Simplicial Schemes, Princeton Univ. Press, 1982. | Zbl | MR

[37] E. Friedlander and B. Parshall, Etale Cohomology of Reductive Groups (Algebraic K-Theory : Evanston. 1980, Springer Lecture Notes in Math., Vol. 854, 1981, pp. 127-140). | Zbl | MR

[38] P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory (Springer Ergebnisse, Vol. 35, 1967). | Zbl | MR

[39] S. M. Gersten, Mayer-Vietoris Functors and Algebraic K-Theory (J. Alg., Vol. 18, 1971, pp. 55-58). | Zbl | MR

[40] S. M. Gersten, Problems about Higher K-Functors (Higher K-Theories, Springer Lecture Notes in Math., Vol. 341, 1973, pp. 43-56). | Zbl | MR

[41] S. M. Gersten, Higher K-Theory of Rings (Higher K-Theories, Springer Lecture Notes in Math., Vol. 341, 1973, pp. 3-42). | Zbl | MR

[42] H. Gillet, Riemann-Roch Theorems for Higher Algebraic K-Theory (Advances in Math., Vol. 40, 1981, pp. 203-289). | Zbl | MR

[43] H. Gillet, Comparison of K-Theory Spectral Sequences, with Applications (Algebraic K-Theory : Evanston. 1980, Springer Lecture Notes in Math., Vol. 854, 1981, pp. 141-167). | Zbl | MR

[44] H. Gillet, On the K-Theory of Surfaces with Multiple Curves, (Duke Math., Journal, Vol. 51, 1984, pp. 195-233). | Zbl | MR

[45] H. Gillet and R. Thomason, The K-Theory of Strict Hensel Local Rings and a Theorem of Suslin (J. Pure Applied Algebra, Vol. 34, 1984, pp. 241-254). | Zbl | MR

[46] R. Godement, Topologie algébrique et Théorie des Faisceaux, Herman, 1958. | Zbl | MR

[47] J. W. Gray, Fibred and Cofibred Categories (Proceedings of the Conference on Categorical Algebra, La Jolla, 1965, Springer, 1966, pp. 21-83). | Zbl | MR

[48] J. W. Gray, Closed Categories, Lax Limits, and Homotopy Limits (J. Pure Appl. Alg., Vol. 19, 1980, pp. 127-158). | Zbl | MR

[49] A. Grothendieck, Sur quelques points d'algèbre homologique (Tohoku Math. J., Vol. 9, 1957, pp. 119-221). | Zbl | MR

[50] R. Hartshorne, Residues and Duality (Springer Lecture Notes in Math., Vol. 20, 1966). | Zbl | MR

[51] R. Hartshorne, Algebraic Geometry (Graduate Texts in Math., Vol. 52, Springer, 1977). | Zbl | MR

[52] A. Heller, Stable Homotopy Categories (Bull. Amer. Math. Soc., Vol. 74, 1968, pp. 28-64). | Zbl | MR

[53] P. J. Hilton and U. Stammbach, A Course in Homological Algebra (Graduate Texts in Math., Vol. 4, Springer, 1971). | Zbl | MR

[54] F. Hirzebruch (Schwarzenberger, Borel), Topological Methods in Algebraic Geometry, 3rd Ed., Grundlehren 131, Springer, 1978. | Zbl | MR

[55] L. Hodgkin, On the K-Theory of Lie Groups (Topology, Vol. 6, 1967, pp. 1-36). | Zbl | MR

[56] L. Illusie, Complexe cotangent et déformations I, II (Springer Lecture Notes in Math., Vol. 239, 1971 and 283, 1972). | Zbl

[57] P. Johnstone, Topos Theory, Academic Press, 1977. | Zbl | MR

[58] J. P. Jouanolou, Une suite exacte de Mayer-Vietoris en K-théorie algébrique (Higher K-Theories, Springer Lecture Notes in Math., Vol. 341, 1973, pp. 293-316). | Zbl | MR

[59] M. Karoubi and O. Villamayor, Foncteurs Kn en algèbre et en topologie (C. R. Acad. Sc., Paris, T. 269, série A, 1969, pp. 416-419). | Zbl | MR

[60] M. Karoubi and O. Villamayor, K-théorie algébrique et K-théorie topologique (Math. Scand., Vol. 28, 1971, pp. 265-307). | Zbl | MR

[61] D. M. Kan, Functors Involving c.s.s. Complexes (Trans. Amer. Math. Soc., Vol. 87, 1958, pp. 330-346). | Zbl | MR

[62] D. M. Kan, Semisimplicial Spectra (Ill. J. Math., Vol. 7, 1963, pp. 463-478). | Zbl | MR

[63] D. M. Latch, A Fibred Homotopy Equivalence and Homology Theories for the Category of Small Categories (J. Pure Appl. Alg., Vol. 15, 1979, pp. 247-269). | Zbl | MR

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