Algebraic K -theory and etale cohomology

R. W. Thomason

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 3, page 437-552
  • ISSN: 0012-9593

How to cite

top

Thomason, R. W.. "Algebraic $K$-theory and etale cohomology." Annales scientifiques de l'École Normale Supérieure 18.3 (1985): 437-552. <http://eudml.org/doc/82164>.

@article{Thomason1985,
author = {Thomason, R. W.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {algebraic -theory in algebraic geometry; Bott element; purity},
language = {eng},
number = {3},
pages = {437-552},
publisher = {Elsevier},
title = {Algebraic $K$-theory and etale cohomology},
url = {http://eudml.org/doc/82164},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Thomason, R. W.
TI - Algebraic $K$-theory and etale cohomology
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 3
SP - 437
EP - 552
LA - eng
KW - algebraic -theory in algebraic geometry; Bott element; purity
UR - http://eudml.org/doc/82164
ER -

References

top
  1. [1] J. F. ADAMS, Stable Homotopy and Generalized Homology, Univ. of Chicago Press, 1974. Zbl0309.55016MR402720
  2. [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). Zbl0129.15201MR182967
  3. [3] M. ARTIN, Grothendieck Topologies (Lecture Notes, Harvard Univ., 1962). Zbl0208.48701
  4. [4] M. ARTIN, On the Joins of Hensel Rings (Advances in Math., Vol. 7, 1971, pp. 282-296). Zbl0242.13021MR289501
  5. [5] M. ARTIN and B. MAZUR, Etale Homotopy (Springer Lecture Notes in Math., Vol. 100, 1969). Zbl0182.26001MR245577
  6. [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. [7] M. BARR, Toposes without Points (J. Pure Appl. Alg., Vol. 5, 1974, pp. 265-280). Zbl0294.18009MR409602
  8. [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). Zbl0475.14015MR575206
  9. [9] A. A. BEILINSON, Visshi regulyatori i znacheniya L-funcni, (Sovremennge Problemy Matematiki, Vol. 24, 1984, pp. 181-238). MR760999
  10. [10] J. M. BOARDMAN, Conditionally Convergent Spectral Sequences, preprint, 1981. Zbl0947.55020MR1718076
  11. [11] A. K. BOUSFIELD, The Localization of Spaces with Respect to Homology (Topology, Vol. 14, 1975, pp. 133-150). Zbl0309.55013MR380779
  12. [12] A. K. BOUSFIELD, The Localization of Spectra with Respect to Homology (Topology, Vol. 18, 1979, pp. 257-281). Zbl0417.55007MR551009
  13. [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). Zbl0511.55007MR647434
  14. [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). Zbl0405.55021MR513569
  15. [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). Zbl0202.22803MR283801
  16. [16] A. K. BOUSFIELD and D. M. KAN, Homotopy Limits, Completions, and Localizations (Springer Lecture Notes in Math., Vol. 304, 1972). Zbl0259.55004MR365573
  17. [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). Zbl0386.18011MR513541
  18. [18] K. S. BROWN, Abstract Homotopy Theory and Generalized Sheaf Cohomology (Trans. Amer. Math. Soc., Vol. 186, 1973, pp. 419-458). Zbl0245.55007MR341469
  19. [19] K. S. BROWN, Cohomology of Groups (Graduate Texts in Math., Vol. 87, Springer, 1982). Zbl0584.20036MR672956
  20. [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). Zbl0291.18017MR347943
  21. [21] H. CARTAN and S. EILENBERG, Homological Algebra, Princeton University Press, 1956. Zbl0075.24305MR77480
  22. [22] E. B. CURTIS, Simplicial Homotopy Theory (Advances in Math., Vol. 6, 1971, pp. 107-209). Zbl0225.55002MR279808
  23. [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). Zbl0462.18006MR618299
  24. [24] P. DELIGNE, Théorie de Hodge III (Publ. Math. I.H.E.S., Vol. 44, 1974, pp. 5-77). Zbl0237.14003MR498552
  25. [25] T. TOM DIECK, Transformation Groups and Representation Theory (Springer Lecture Notes in Math., Vol. 766, 1979). Zbl0445.57023MR551743
  26. [26] A. DOLD, Homology of Symmetric Products and Other Functors of Complexes (Ann. Math., Vol. 68, 1958, pp. 54-80). Zbl0082.37701MR97057
  27. [27] A. DOLD and D. PUPPE, Homologie Nich-Additive-Funktoren. Anwendungen (Ann. Inst. Fourier, Vol. 11, 1961, pp. 201-312). Zbl0098.36005MR150183
  28. [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). Zbl0331.18016MR384917
  29. [29] E. DUBUC, Kan Extensions in Enriched Category Theory (Springer Lectures Notes in Math., Vol. 145, 1970). Zbl0228.18002MR280560
  30. [30] W. DWYER and E. FRIEDLANDER, Etale K-Theory and Arithmetic, preprint, 1983. MR648533
  31. [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). Zbl0501.14013MR662604
  32. [32] E. DYER, Cohomology Theories, Benjamin, 1969. Zbl0182.57002MR268883
  33. [33] E. FRIEDLANDER, Computations of K-Theories of Finite Fields (Topology, Vol. 15, 1976, pp. 87-109). Zbl0401.18007MR394660
  34. [34] E. FRIEDLANDER, Etale K-Theory I : Connections with Etale Cohomology and Algebraic Vector Bundles (Invent. Math., Vol. 60, 1980, pp. 105-134). Zbl0519.14010MR586424
  35. [35] E. FRIEDLANDER, Etale K-Theory II : Connections with Algebraic K-Theory (Ann. scient. Ec. Norm. Sup., Vol. 15, 1982, pp. 231-256). Zbl0537.14011MR683636
  36. [36] E. FRIEDLANDER, Etale Homotopy of Simplicial Schemes, Princeton Univ. Press, 1982. Zbl0538.55001MR676809
  37. [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). Zbl0495.14029MR618302
  38. [38] P. GABRIEL and M. ZISMAN, Calculus of Fractions and Homotopy Theory (Springer Ergebnisse, Vol. 35, 1967). Zbl0186.56802MR210125
  39. [39] S. M. GERSTEN, Mayer-Vietoris Functors and Algebraic K-Theory (J. Alg., Vol. 18, 1971, pp. 55-58). Zbl0215.09801MR280570
  40. [40] S. M. GERSTEN, Problems about Higher K-Functors (Higher K-Theories, Springer Lecture Notes in Math., Vol. 341, 1973, pp. 43-56). Zbl0285.18011MR338125
  41. [41] S. M. GERSTEN, Higher K-Theory of Rings (Higher K-Theories, Springer Lecture Notes in Math., Vol. 341, 1973, pp. 3-42). Zbl0285.18010MR382398
  42. [42] H. GILLET, Riemann-Roch Theorems for Higher Algebraic K-Theory (Advances in Math., Vol. 40, 1981, pp. 203-289). Zbl0478.14010MR624666
  43. [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). Zbl0478.14011MR618303
  44. [44] H. GILLET, On the K-Theory of Surfaces with Multiple Curves, (Duke Math., Journal, Vol. 51, 1984, pp. 195-233). Zbl0557.14003MR744295
  45. [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). Zbl0577.13009MR772059
  46. [46] R. GODEMENT, Topologie algébrique et Théorie des Faisceaux, Herman, 1958. Zbl0080.16201MR102797
  47. [47] J. W. GRAY, Fibred and Cofibred Categories (Proceedings of the Conference on Categorical Algebra, La Jolla, 1965, Springer, 1966, pp. 21-83). Zbl0192.10701MR213413
  48. [48] J. W. GRAY, Closed Categories, Lax Limits, and Homotopy Limits (J. Pure Appl. Alg., Vol. 19, 1980, pp. 127-158). Zbl0462.55008MR593251
  49. [49] A. GROTHENDIECK, Sur quelques points d'algèbre homologique (Tohoku Math. J., Vol. 9, 1957, pp. 119-221). Zbl0118.26104MR102537
  50. [50] R. HARTSHORNE, Residues and Duality (Springer Lecture Notes in Math., Vol. 20, 1966). Zbl0212.26101MR222093
  51. [51] R. HARTSHORNE, Algebraic Geometry (Graduate Texts in Math., Vol. 52, Springer, 1977). Zbl0367.14001MR463157
  52. [52] A. HELLER, Stable Homotopy Categories (Bull. Amer. Math. Soc., Vol. 74, 1968, pp. 28-64). Zbl0177.25605MR224090
  53. [53] P. J. HILTON and U. STAMMBACH, A Course in Homological Algebra (Graduate Texts in Math., Vol. 4, Springer, 1971). Zbl0238.18006MR346025
  54. [54] F. HIRZEBRUCH (SCHWARZENBERGER, BOREL), Topological Methods in Algebraic Geometry, 3rd Ed., Grundlehren 131, Springer, 1978. Zbl0376.14001MR1335917
  55. [55] L. HODGKIN, On the K-Theory of Lie Groups (Topology, Vol. 6, 1967, pp. 1-36). Zbl0186.57103MR214099
  56. [56] L. ILLUSIE, Complexe cotangent et déformations I, II (Springer Lecture Notes in Math., Vol. 239, 1971 and 283, 1972). Zbl0238.13017
  57. [57] P. JOHNSTONE, Topos Theory, Academic Press, 1977. Zbl0368.18001MR470019
  58. [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). Zbl0291.14006MR409476
  59. [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). Zbl0182.57001MR251717
  60. [60] M. KAROUBI and O. VILLAMAYOR, K-théorie algébrique et K-théorie topologique (Math. Scand., Vol. 28, 1971, pp. 265-307). Zbl0231.18018MR313360
  61. [61] D. M. KAN, Functors Involving c.s.s. Complexes (Trans. Amer. Math. Soc., Vol. 87, 1958, pp. 330-346). Zbl0090.39001MR131873
  62. [62] D. M. KAN, Semisimplicial Spectra (Ill. J. Math., Vol. 7, 1963, pp. 463-478). Zbl0115.40401MR153017
  63. [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). Zbl0407.55006MR537499

Citations in EuDML Documents

top
  1. Fabien Morel, Vladimir Voevodsky, A 1 -homotopy theory of schemes
  2. Jens Hornbostel, Guido Kings, On non-commutative twisting in étale and motivic cohomology
  3. Joël Riou, Catégorie homotopique stable d’un site suspendu avec intervalle
  4. M. A. Batanin, Coherent categories with respect to monads and coherent prohomotopy theory
  5. Joseph Tapia, K -théorie algébrique négative et K -théorie topologique de l’algèbre de Fréchet des opérateurs régularisants
  6. Wiesława Nizioł, Crystalline conjecture via K -theory

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.