Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bloch, S., Algebraic K-theory and class field theory for arithmetic surfaces, Ann. of Math. 114, 1981, 229–266.
Coombes, K.R., Algebraic K-theory and abelianized fundamental groups of curves, preprint.
Illusie, L., Complexe de De Rham-Witt et cohomologie cristalline, Ann. Sci. Ec. Norm. Sup. 12, 1979, 501–661.
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.
Kato, K., Galois cohomology of complete discrete valuation fields, to appear.
Kato, K., The existence theorem for higher local class field theory, preprint.
Kato, K. and Saito, S., Unramified class field theory of arithmetical surfaces, preprint.
Kato, K. and Saito, S., Two dimensional class field theory, preprint.
Katz, N. and Lang, S., Finiteness theorems in geometric class field theory, to appear.
Lang, S., Unramified class field theory over function fields in several variables, Ann. of Math. 64, 1956, 285–325.
Lang, S., Sur les séries L d’une variété algébrique, Bull. Soc. Math. de France, 84, 1956, 385–407.
Lichtenbaum, S., Duality theorems for curves over p-adic fields, Invent. math. 7, 1969, 120–136.
Milnor, J., Algebraic K-theory and quadratic forms, Invent. math. 9, 1970, 318–344.
Paršin, A.N., Class fields and algebraic K-theory, Uspehi Mat. Nauk 30, 1975, no. 1, 253–254.
Saito, S., The class field theory for curves over local fields, preprint.
Saito, S., The arithmetic on two dimensional complete local rings, Master’s thesis, Univ. of Tokyo, 1982.
Saito, S., Unramified class field theory of arithmetic schemes, preprint.
Serre, J.-P., Groupes algébriques et corps de classes, Publ. Inst. Math. Nancago, Hermann, 1959.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0099960
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12685-0
Online ISBN: 978-3-540-38676-6
eBook Packages: Springer Book Archive