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Cycles algébriques de torsion et K-théorie algébrique Cours au C.I.M.E., juin 1991

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Bibliographie

  1. L. Barbieri-viale. — Cohomology theories and algebraic cycles on singular varieties, Contemp. Math. 126 (1992) 197–217; Theorie coomologiche e cicli algebrici sulle varieta' singolari, Tesi di dottorato, Universita' di Genova (1991).

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Bloch. — Torsion algebraic cycles and a theorem of Roitman, Comp. Math. 39 (1979) 107–127.

    MathSciNet  MATH  Google Scholar 

  3. S. Bloch. — Lectures on algebraic cycles, Duke Univ. Math. Ser. 4, Durham, N.C. 1980.

    Google Scholar 

  4. S. Bloch. — Torsion algebraic cycles, K2 and Brauer groups of function fields, in L.N.M. 844 (ed. M. Kervaire et M. Ojanguren) Springer 1981.

    Google Scholar 

  5. S. Bloch. — On the Chow groups of certain rational surfaces, Ann. Sc. Ec. Norm. Sup. 14 (1981) 41–59.

    MathSciNet  MATH  Google Scholar 

  6. S. Bloch. — Algebraic K-theory and class field theory for arithmetic surfaces, Ann. of Math. 114 (1981) 229–265.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Bloch and A. Ogus. — Gersten's conjecture and the homology of schemes, Ann. Sc. E.N.S. 7 (1974) 181–202.

    MathSciNet  MATH  Google Scholar 

  8. S. Bloch and V. Srinivas. — Remarks on correspondences and algebraic cycles, Am. J. Math. 105 (1983) 1235–1253.

    Article  MathSciNet  MATH  Google Scholar 

  9. J.-L. Colliot-Thélène. — Hilbert's theorem 90 for K2, with application to the Chow group of rational surfaces, Invent. Math. 35 (1983) 1–20.

    Article  MATH  Google Scholar 

  10. J.-L. Colliot-Thélène. — On the reciprocity sequence in higher class field theory of function fields, Prépublication d'Orsay 92-52 (1992).

    Google Scholar 

  11. J.-L. Colliot-Thélène and W. Raskind. — K2-cohomology and the second Chow group, Math. Ann. 270 (1985) 165–199.

    Article  MathSciNet  MATH  Google Scholar 

  12. J.-L. Colliot-Thélène and W. Raskind. — On the reciprocity law for surfaces over finite fields, J. Fac. Sc. Univ. Tokyo, Sect. IA 33 (1986) 283–294.

    MathSciNet  MATH  Google Scholar 

  13. J.-L. Colliot-Thélène et W. Raskind. — Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: un théorème de finitude pour la torsion, Invent. Math. 105 (1991) 221–245.

    Article  MathSciNet  MATH  Google Scholar 

  14. J.-L. Colliot-Thélène and J.-J. Sansuc. — On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch, Duke Math. J. 48 (1981) 421–447.

    Article  MathSciNet  MATH  Google Scholar 

  15. J.-L. Colliot-Thélène, J.-J. Sansuc et C. Soulé. — Torsion dans le groupe de Chow de codimension deux, Duke Math. J. 50 (1983) 763–801.

    Article  MathSciNet  MATH  Google Scholar 

  16. K. Coombes. — The arithmetic of zero-cycles on surfaces with geometric genus and irregularity zero, Math. Ann. 291 (1991) 429–452.

    Article  MathSciNet  MATH  Google Scholar 

  17. W. Fulton. — Intersection Theory, Ergeb. der Math. und ihr. Grenzgeb. 3. Folge, Bd. 2, Springer 1984.

    Google Scholar 

  18. M. Gros. — 0-cycles de degré zéro sur les surfaces fibrées en coniques, J. reine und angew. Math. 373 (1987) 166–184.

    MathSciNet  MATH  Google Scholar 

  19. M. Gros et N. Suwa. — Application d'Abel-Jacobi p-adique et cycles algébriques, Duke Math. J. 57 (1988) 579–613.

    Article  MathSciNet  MATH  Google Scholar 

  20. U. Jannsen. — On the l-adic cohomology of varieties over number fields and its Galois cohomology, in: Galois groups overQ (ed. Y. Ihara, K. Ribert, J.-P. Serre) Springer-Verlag 1987.

    Google Scholar 

  21. K. Kato. — A Hasse principle for two dimensional global fields, J. für die reine und angew. Math. 366 (1986) 142–181.

    MathSciNet  MATH  Google Scholar 

  22. K. Kato and S. Saito. — Unramified class field theory of arithmetical surfaces, Ann. of Math. 118 (1983) 241–275.

    Article  MathSciNet  MATH  Google Scholar 

  23. F. Lecomte. — Rigidité des groupes de Chow, Duke Math. J. 53 (1986) 405–426.

    Article  MathSciNet  MATH  Google Scholar 

  24. A.S. Merkur'ev and A.A. Suslin. — K-cohomology of Severi-Brauer varieties and norm residue homomorphism, Izv. Akad. Nauk SSSR 46 (1982) 1011–1146 = Math. USSSR Izv. 21 (1983) 307–341.

    MathSciNet  MATH  Google Scholar 

  25. J.S. Milne. — Etale cohomology, Princeton University Press, 33, Princeton, N.J. 1980.

    Google Scholar 

  26. J.S. Milne. — Arithmetic Duality Theorems, Perspect. Math. 1, Academic Press, Boston 1986.

    MATH  Google Scholar 

  27. D. Quillen. — Higher algebraic K-theory I, in Algebraic K-theory I (H. Bass, ed.) LNM 341, Springer-Verlag 1973.

    Google Scholar 

  28. W. Raskind. — Algebraic K-theory, étale cohomology and torsion algebraic cycles, in Algebraic K-theory and Algebraic Number Theory, Honolulu 1987, Contemporary Mathematics 83 (1989) 311–341.

    Google Scholar 

  29. W. Raskind. — Torsion algebraic cycles on varieties over local fields, in: Algebraic K-theory: Connections with Geometry and Topology, Lake Louise 1987, (J.F. Jardine and V.P. Snaith, ed.) Kluwer Academic Publishers 1989.

    Google Scholar 

  30. W. Raskind. — On K1 of curves over global fields, Math. Ann. 288 (1990) 179–193.

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Saito. — A global duality theorem for varieties over global fields, in: Algebraic K-theory: Connections with Geometry and Topology, Lake Louise 1987, (J.F. Jardine and V.P. Snaith, ed.) Kluwer Academic Publishers 1989.

    Google Scholar 

  32. S. Saito. — A conjecture of Bloch and Brauer groups of surfaces over p-adic fields, preprint, May 1990.

    Google Scholar 

  33. S. Saito. — Torsion zero-cycles and étale homology of singular schemes, Duke Math. J. 64 (1991) 71–83.

    Article  MathSciNet  MATH  Google Scholar 

  34. S. Saito. — Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991) 443–460.

    Article  MathSciNet  MATH  Google Scholar 

  35. P. Salberger. — Zero-cycles on rational surfaces over number fields, Invent. Math. 91 (1988) 505–524.

    Article  MathSciNet  MATH  Google Scholar 

  36. P. Salberger. — Chow groups of codimension two and l-adic realizations of motivic cohomology, typescript, September 1991.

    Google Scholar 

  37. C. Schoen. — Some examples of torsion in the Griffiths group, Math. Ann. 293 (1992) 651–679.

    Article  MathSciNet  MATH  Google Scholar 

  38. M. Somekawa. — On Milnor K-groups attached to semi-abelian varieties, Journal of K-theory 4 (1990) 105–119.

    Article  MathSciNet  MATH  Google Scholar 

  39. C. Soulé. — K2 et le groupe de Brauer [d'après A.S. Merkurjev et A.A. Suslin], Séminaire Bourbaki, 1982/83, no601.

    Google Scholar 

  40. V. Srinivas. — Rational equivalence of 0-cycles on normal varieties over C, Proceedings of Symposia in Pure Mathematics 46, Part 2, (1987) 475–482.

    Article  MathSciNet  Google Scholar 

  41. A.A. Suslin. — Torsion in K2 of fields, Journal of K-theory 1 (1987) 5–29.

    Article  MathSciNet  MATH  Google Scholar 

  42. N. Suwa. — Sur l'image de l'application d'Abel-Jacobi de Bloch, Bull. Soc. Math. France 116 (1988) 69–101.

    MathSciNet  MATH  Google Scholar 

  43. Cohomologie étale, Séminaire de Géométrie Algébrique du Bois-Marie SGA 4 1/2, par P. Deligne, Springer L.N.M. 569 (1977).

    Google Scholar 

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Edoardo Ballico

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Colliot-Thélène, JL. (1993). Cycles algébriques de torsion et K-théorie algébrique Cours au C.I.M.E., juin 1991. In: Ballico, E. (eds) Arithmetic Algebraic Geometry. Lecture Notes in Mathematics, vol 1553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084728

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