Skip to main content
Log in

K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliographie

  1. Artin, M.: Grothendieck Topologies. Springer 1962

  2. Artin, M., Verdier, J.L.: Seminar on Etale Cohomology of number fields. AMS Summer Institute on Algebraic geometry 1964

  3. Bayer, P., Neukirch, J.: On values of zeta functions and ℓ-adic Euler characteristics. Inventiones math.50, 35–64 (1978)

    Google Scholar 

  4. Bass, H.: AlgebraicK-theory. New York: Benjamin 1968

    Google Scholar 

  5. Bass, H., Tate, J.: The Milnor ring of a global field. “AlgebraicK-theory II”. Lecture Notes in Mathematics no. 342. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  6. Bloch, S.: Higher regulators, AlgebraicK-theory, and zeta functions of elliptic curves. Preprint

  7. Bloch, S.: AlgebraicK-theory and crystalline cohomology, I.H.E.S., no 47, 187–268 (1978)

    Google Scholar 

  8. Bloch, S.: Some formulas pertaining to theK-theory of commutative groupschemes. Preprint, 1977

  9. Bloch, S., Ogus, A.: Gersten's Conjecture and the homology of schemes. Ann. Scient. Ec. Norm. Sup.,7, fasc. 2 (1974)

    Google Scholar 

  10. Borel, A.: Stable real cohomology of arithmetic groups. Ann. Scient. Ec. Norm. Sup., 4è série,7, 235–272 (1974)

    Google Scholar 

  11. Browder, W.: AlgebraicK-theory with coefficientsZ/p, dans “Geometry applications of Homotopy Theory I”. Lecture notes in Mathematics no. 657. Berlin-Heidelberg-New York: Springer 1978

    Google Scholar 

  12. Cartan, E., Eilenberg, S.: Homological Algebra, Princeton University Press, 1956

  13. Cassels, J.W., Fröhlich, A.: Algebraic Number Theory. New York-London: Academic Press, 1967

    Google Scholar 

  14. Charney, R.: Homology Stability forGL n of a Dedekind domain, à paraître

  15. Coates, J., Lichtenbaum, S.: On ℓ-adic zêta functions. Annals of Maths.,98, 498–550 (1973)

    Google Scholar 

  16. Deligne, P., Ribet, K.: Values of abelianL-functions at negative integers, à paraître aux Inventiones math.

  17. Farrell, F.T., Hsiang, W.C.: On the rational homotopy groups of the diffeomorphisms groups of discs, spheres and aspherical manifolds.

  18. Ferrero, B., Washington, L.C.: The Iwasawa invariantμ p for abelian number fields. A paraître aux Annals of Maths.

  19. Gillet, H.: The applications of AlgebraicK-theory to intersection theory. Thèse, preprint

  20. Grayson, D.: Higher AlgebraicK-theory II. Lecture notes in Mathematics no 551. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  21. Grothendieck, A.: Classes de Chern et représentations linéaires des groupes discrets. Dans «10 exposés sur la cohomologie des schémas». Masson: North-Holland 1968

    Google Scholar 

  22. Grothendieck, A.: Eléments de Géométrie Algébrique, Chapitre 0, §13, Publications I.H.E.S. no 11, 1961

  23. Harris, B., Segal, G.:K i of rings of algebraic integers. Ann. of Maths.101, 20–33 (1975)

    Google Scholar 

  24. Hiller, H.: λ-rings and algebraicK-theory. Preprint

  25. Illusie, L.: Lettre à Gersten, 24/2/1974

  26. Karoubi, M.: A paraître

  27. Kato, K.: A generalization of local class field theory by usingK-groups, I et II. Proc. Japan Acad.53, 140–143 (1977)54, 250–255 (1979)

    Google Scholar 

  28. Kratzer, C.: Opérations d'Adams enK-théorie algébrique, Note aux C.R. Acad. Sc. Paris,287, Série A, 297 (1978) et article en préparation

  29. Lee, R., Szczarba, R.H.: The groupK 3(ℤ) is cyclic of order 48, Ann. of Math.,104, 31–60 (1976)

    Google Scholar 

  30. Lee, R., Szczarba, R.H.: On the torsion inK 4(ℤ) andK 5(ℤ). Duke Journal, 1978

  31. Lichtenbaum, S.: On the values of zéta andL-functions, I. Ann. of Maths.,96, 338–360 (1972)

    Google Scholar 

  32. Lichtenbaum, S.: Values of zeta functions, étale cohomology, and algebraicK-theory. Dans “Alg.K-theory II”. Lecture notes in Mathematics no 342. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  33. Loday, J.L.:K-théorie et représentations de groupes. Ann. Scient. Ec. Norm. Sup. 4ème série,9, 309–377 (1976)

    Google Scholar 

  34. Maazen, H.: Stabilité de l'homologie deGL n . C.R. Acad. Sc. Paris,288, 707–708 (1979)

    Google Scholar 

  35. Milnor, J.: Introduction to AlgebraicK-theory. Annals of Maths. Studies no 72. Princeton

  36. Milnor, J., Stasheff, J.D.: Characteristic classes; Appendice, Annals of Maths. Studies, no67, 1974

  37. Parshin, A.I.: Corps de classes etK-théorie algébrique, Ouspekhi Math. N.T. 30,1, 253–254 (1975) (en russe), et «Class Field Theory for Arthmetical schemes», preprint

    Google Scholar 

  38. Quillen, D.: AlgebraicK-theory I. Lecture Notes no 341

  39. Quillen, D.: On the cohomology andK-theory of the general linear groups over a finite field. Annals of Maths.,96, 552–586 (1972)

    Google Scholar 

  40. Quillen, D.: Lettre à Milnor sur\(\operatorname{Im} (\pi _i O\mathop \to \limits^J \pi _i^s \to K_i \mathbb{Z})\). Lecture Notes in Mathematics no 551. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  41. Quillen, D.: Finite generation of the groupsK i of rings of algebraic integers. Lecture Notes in Mathematics no 341, pp. 179–210. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  42. Quillen, D.: Cours à M.I.T., 1974–75

  43. Raynaud, M.: Caractéristique d'Euler Poincaré d'un faisceau et cohomologie des variétés abéliennes, dans «dix exposés sur la cohomologie des schémas», north Holland: Masson 1968

  44. Séminaire de Géométrie Algébrique IV: Exposé VIII, A. Grothendieck, Lecture notes in Mathematics no 270. Berlin-Heidelberg-New York: Springer 1972

  45. S.G.A. IV 1/2: Cohomologie étale: les points de départ, par P. Deligne, rédigé par J.F. Boutot. Lecture notes in Mathematics no 569. Berlin-Heidelberg-New York: Springer 1977

  46. Serre, J-P.: Corps locaux. Hermann, Act. Scient. et Ind., 1968

  47. Serre, J-P.: Cohomologie galoisienne. Lecture notes in Mathematics no. 5. Berlin-Heidelberg-New York: Springer 1964

    Google Scholar 

  48. Serre, J-P.: Homologie singulière des espaces fibrés. Applications. Ann. of Maths. (2)54, 425–505 (1951)

    Google Scholar 

  49. Serre, J-P.: Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures). Séminaire Delange-Poitou-Pisot no 19, 1969/70

  50. Soulé, C.: Addendum to the article «On the torsion inK *(ℤ)». Duke Journal, pp. 131–132 (1978)

  51. Soulé, C.: Classes de torsion dans la cohomologie des groupes arithmétiques. C.R. Acad. Sc. Paris,284, 1009–1011 (1977)

    Google Scholar 

  52. Soulé, C.:K-théorie de ℤ et cohomologie étale. C.R. Acad. Sc. Paris,286, 1179–1181 (1978)

    Google Scholar 

  53. Soulé, C.: Groupes arithmétiques etK-théorie des anneaux d'entiers de corps de nombres. Thèse, Paris VII, 1978

  54. Tate, J.: Relations betweenK 2 and Galois cohomology. Inventiones Math.,36, 257–274 (1976)

    Google Scholar 

  55. Tate, J.: Algebraic cycles and poles of zeta functions, dans «Arithmetical Algebraic Geometry» (O.F.G. Schilling ed.), p. 93, 1963

  56. Wagstaff, S.: The irregular primes to 125000. Math. Computations, p. 583, A.M.S. 1978

  57. Waldhausen, F.: AlgebraicK-theory of generalized free products, I et II. Annals of Maths.,108, 135–204, 205–256 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Soulé, C. K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale. Invent Math 55, 251–295 (1979). https://doi.org/10.1007/BF01406843

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01406843

Navigation