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Class field theory and algebraic K-theory

  • P-adic Methods In Algebraic Geometry And Arithmetic
  • Conference paper
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Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1016))

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References

  1. Bloch, S., Algebraic K-theory and class field theory for arithmetic surfaces, Ann. of Math. 114, 1981, 229–266.

    Article  MathSciNet  MATH  Google Scholar 

  2. Coombes, K.R., Algebraic K-theory and abelianized fundamental groups of curves, preprint.

    Google Scholar 

  3. Illusie, L., Complexe de De Rham-Witt et cohomologie cristalline, Ann. Sci. Ec. Norm. Sup. 12, 1979, 501–661.

    MathSciNet  MATH  Google Scholar 

  4. Kato, K., A generalization of local class field theory by using K-groups, I, J. Fac. Sci. Univ. of Tokyo, Sec. IA, 26, 1979, 303–376, II, ibid. 27, 1980, 603–683, III, ibid. 29, 1982, 31–43.

    MathSciNet  MATH  Google Scholar 

  5. Kato, K., Galois cohomology of complete discrete valuation fields, to appear.

    Google Scholar 

  6. Kato, K., The existence theorem for higher local class field theory, preprint.

    Google Scholar 

  7. Kato, K. and Saito, S., Unramified class field theory of arithmetical surfaces, preprint.

    Google Scholar 

  8. Kato, K. and Saito, S., Two dimensional class field theory, preprint.

    Google Scholar 

  9. Katz, N. and Lang, S., Finiteness theorems in geometric class field theory, to appear.

    Google Scholar 

  10. Lang, S., Unramified class field theory over function fields in several variables, Ann. of Math. 64, 1956, 285–325.

    Article  MathSciNet  MATH  Google Scholar 

  11. Lang, S., Sur les séries L d’une variété algébrique, Bull. Soc. Math. de France, 84, 1956, 385–407.

    MATH  Google Scholar 

  12. Lichtenbaum, S., Duality theorems for curves over p-adic fields, Invent. math. 7, 1969, 120–136.

    Article  MathSciNet  MATH  Google Scholar 

  13. Milnor, J., Algebraic K-theory and quadratic forms, Invent. math. 9, 1970, 318–344.

    Article  MathSciNet  MATH  Google Scholar 

  14. Paršin, A.N., Class fields and algebraic K-theory, Uspehi Mat. Nauk 30, 1975, no. 1, 253–254.

    MathSciNet  Google Scholar 

  15. Saito, S., The class field theory for curves over local fields, preprint.

    Google Scholar 

  16. Saito, S., The arithmetic on two dimensional complete local rings, Master’s thesis, Univ. of Tokyo, 1982.

    Google Scholar 

  17. Saito, S., Unramified class field theory of arithmetic schemes, preprint.

    Google Scholar 

  18. Serre, J.-P., Groupes algébriques et corps de classes, Publ. Inst. Math. Nancago, Hermann, 1959.

    MATH  Google Scholar 

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Michel Raynaud Tetsuji Shioda

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© 1983 Springer-Verlag

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Kato, K. (1983). Class field theory and algebraic K-theory. In: Raynaud, M., Shioda, T. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 1016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099960

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  • DOI: https://doi.org/10.1007/BFb0099960

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  • Print ISBN: 978-3-540-12685-0

  • Online ISBN: 978-3-540-38676-6

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