References
[A] Artin, M.: Dimension cohomologique: Premiers résultats, in: Théorie des topos et cohomologie étale des schémas, Tome 3. (Lecture Notes in Math., Vol. 305, pp. 43–63 Berlin, Heidelberg, New York: Springer 1973
[Be] Beilinson, A.: Height pairings between algebraic cycles To appear in Proc. Boulder Conf. on algebraicK-theory
[B1] Bloch, S.: Algebraic cycles and higherK-theory. Preprint, IHES (1985)
[B-M-S] Beilinson, A., MacPherson, R., Schechtman, V.: Notes on motivic cohomology. Preprint
[B-T] Bass, H., Tate, J.: The Milnor ring of a global field. (Lecture Notes in Math., Vol. 342, pp. 349–446) Berlin, Heidelberg, New York: Springer 1972
[C-S-S] Colliot-Thélèane, J.-L., Sansuc, J.-J., Swinnerton-Dyer, P.: Intersections of two quardrics and Châtelet surfaces. J. Reine Angew. Math.373, 37–107 (1987),374, 72–168 (1987)
[G] Grothendieck, A.: Le groupe de Brauer I et II, in: Dix exposés sur la cohomologie des schémas. Amsterdam: North-Holland 1968
[I] Illusie, L.: Complexe de De Rham-Witt et cohomologie cristalline. Ann. Sci. Norm. Super. Pisa, Cl. Sci., IV. Ser. 12, 501–661 (1979)
[K-1] Kato, K.: A generalization of local class field theory by usingK-groups I. J. Fac. Sci. Univ. Tokyo, Sec. IA,26, 303–376 (1979); II. ibid. Kato, K.: A generalization of local class field theory by usingK-groups I. J. Fac. Sci. Univ. Tokyo, Sec. IA27, 603–683 (1980); III. ibid. Kato, K.: A generalization of local class field theory by usingK-groups I. J. Fac. Sci. Univ. Tokyo, Sec. IA29, 31–43 (1982)
[K-2] Kato, K.: Galois cohomology of complete discrete valuation fields. (Lecture Notes in Math. Vol. 967, pp. 215–238. Berlin, Heidelberg, New York: Springer 1982
[K-3] Kato, K.: The existence theorem for higher local class field theory. Preprint
[K-4] Kato, K.: MilnorK-theory and the Chow group of zero-cycles. Contemp. Math.55, 241–253 (1986)
[K-5] Kato, K.: A Hasse principle for two dimensional global fields. J. Reine, Angew. Math. 366, 142–183 (1986)
[K-S] Kato, K., Saito, S.: Global class field theory of arithmetic schemes. Contemp. Math.55, 255–331 (1986)
[L-1] Lichtenbaum, S.: Values of zeta functions at non-negative integers. In: Number Theory. (Lecture Notes in Math., Vol. 1068, pp. 127–138). Berlin, Heidelberg, New York: Springer 1984
[L-2] Lichtenbaum, S.: The construction of weight-two arithmetic cohomology. Invent. Math.88, 183–215 (1987)
[L-3] Lichtenbaum, S.: Duality theorems for curves overp-adic fields. Invent. Math.7, 120–136 (1969)
[M-1] Milne, J.: Etale Cohomology. Princeton Univ. Press. 1980
[M-2] Milne, J.: Motivic cohomology and values of zeta functions. Compos., Math.68, 59–102 (1988)
[Ma] Manin, Yu.I.: Le groupe de Brauer-Grothendieck en géométrie diophatienne. Actes du congrès intern. Math. Nice,1, 401–411 (1970)
[Me] Merkurjev, A.S.: On the torsion ofK 2 of local fields. Ann. Math.118, 375–381 (1983)
[N] Nisnevich, A.: Arithmetic and cohomology invariants of semisimple group schemes and compactifications of locally symmetric spaces. Funct. Anal. appl.14, 61–62 (1980)
[Sa-1] Saito, S.: Class field theory for curves over local fields. J. Number Theory21, 44–80 (1985)
[Sa-2] Saito, S.: Arithmetic on two dimensional local rings. Invent. Math.85, 379–414 (1986)
[Sa-3] Saito, S.: Unramified class field theory of arithmetical schemes. Ann. Math.121, 251–281 (1985)
[Sa-4] Saito, S.: Arithmetic theory on an arithmetic surface. Ann. Math.129, 547–589 (1989)
[Sal] Salberger, P.: Zero-cycles on rational surfaces over number fields. Invent. Math.91, 505–524 (1988)
[San] Sansuc, J.-J.: Principe de Hasse, surfaces cubiques et intersections de deux quadriques, exposé aux Journées arithmétiques de Besançon (1985). Astèrisque 147–148 183–207 (1987)
[Se-1] Serre, J.-P.: Cohomologie Galoisienne. (Lecture Notes in Math., Vol. 5). Berlin, Heidelberg, New York: Springer 1965
[Se-2] Serre, J.-P.: Corps Locaux. Paris: Hermann 1962
[Su] Suslin, A.A.: Torsion inK 2 of fields, Lomi Preprint E-2-82, USSR Academy of Sciences, Steklov Mathematical Institute, Leningrad Department
[T-1] Tate, J.: On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. In: Dix Exposés sur la cohomologie des schémas, pp. 189–214. Amsterdam North-Holland 1968
[T-2] Tate, J.: Algebraic cycles and poles of zeta functions, Arithmetic Algebraic Geometry. New York: Harper and Row 1965
[T-3] Tate, J.: Symbols in arithmetic Actes Congrès Intern. Math. Nice, 1, 201–211 (1970)
[T-4] Tate, J.: On the torsion inK 2 of fields. In: Algebraic Number Theory, Papers contributed for the International Symposium, Kyoto (1976), pp. 243–261
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Saito, S. Some observations on motivic cohomology of arithmetic schemes. Invent Math 98, 371–404 (1989). https://doi.org/10.1007/BF01388859
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DOI: https://doi.org/10.1007/BF01388859