Proceedings of the Japan Academy, Series A, Mathematical Sciences

A generalization of local class field theory by using $K$-groups, II

Kazuya Kato

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Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 54, Number 8 (1978), 250-255.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195517586

Digital Object Identifier
doi:10.3792/pjaa.54.250

Mathematical Reviews number (MathSciNet)
MR517332

Zentralblatt MATH identifier
0411.12013

Subjects
Primary: 14K10: Algebraic moduli, classification [See also 11G15] 12B25
Secondary: 32N05: General theory of automorphic functions of several complex variables

Citation

Kato, Kazuya. A generalization of local class field theory by using $K$-groups, II. Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), no. 8, 250--255. doi:10.3792/pjaa.54.250. https://projecteuclid.org/euclid.pja/1195517586


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References

  • [1] H. Bass and J. Tate: The Milnor ring of a global field. Lect. Notes in Math., Springer-Verlag, Berlin, vol.342, pp. 349-446 (1972).
  • [2] S. Bloch: Algebraic K-theory and crystalline cohomology. Publ. Math. I.H.E.S., 47, 187-268 (1978).
  • [3] D. Grayson: Higher algebraic K-theory. II. Lect. Notes in Math., Springer-Verlag, Berlin, vol.551, pp. 217-240 (1976).
  • [4] A. Grothendieck: Elements de geometrie algebrique. IV. Premiere partie, Publ. Math. I.H.E.S., 20 (1964).
  • [5] K. Kato: A generalization of local class field theory by using K-groups. I. Proc. Japan Acad., 53, 140-143 (1977).
  • [6] J.-L. Loday: K-theorie algebrique et representations de groupes. Ann. Sci. Ec. Norm. Sup., 4eme serie, 9(3) (1976).
  • [7] J. Milnor: Algebraic K-theory and quadratic forms. Invent. Math., 9, 318- 344 (1970).
  • [8] A.-N. Parsin: Class field theory for arithmetical schemes (preprint).
  • [9] D. Quillen: Higher algebraic K-theory. I. Lect. Notes in Math., Springer-Verlag, Berlin, vol.341, pp. 85-147 (1972).
  • [10] J.-P. Serre: Cohomologie Galoisienne. Springer-Verlag, Berlin (1964).
  • [11] J. Tate: Symbols in arithmetic. Actes du Congres International des Mathematiciens 1970, Gauthier-Villars, Paris, vol.1, pp. 201-211 (1971).
  • [12] E. Witt: Zyklische Korper und Algebren der Charakteristik p vom Grade pn. J. Reine Angew. Math., 176, 126-140 (1936).

See also

  • Part I: Kazuya Kato. A generalization of local class field theory by using $K$-groups, I. Proc. Japan Acad. Ser. A Math. Sci., Volume 53, Number 4 (1977), 140--143.