Milnor, John W. [Tate, John] Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate. (English) Zbl 0199.55501 Invent. Math. 9, 318-344 (1970). Reviewer: J. Burroughs Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 ReviewsCited in 221 Documents MathOverflow Questions: Is there a clean definition of the residue map in Milnor K-theory? MSC: 19G12 Witt groups of rings 11E70 \(K\)-theory of quadratic and Hermitian forms 19C30 \(K_2\) and the Brauer group 14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry Keywords:algebraic geometry Citations:Zbl 0217.34902 PDF BibTeX XML Cite \textit{J. W. Milnor}, Invent. Math. 9, 318--344 (1970; Zbl 0199.55501) Full Text: DOI EuDML OpenURL References: [1] Artin, E.: Algebraic numbers and algebraic functions. New York: Gordon and Breach 1967. · Zbl 0194.35301 [2] Bass, H.:K 2 and symbols, pp. 1-11 of AlgebraicK-theory and its geometric applications. Lecture Notes in Mathematics, Vol.108. Berlin-Heidelberg-New York: Springer 1969. [3] Bass, H.: Tate, J.:K 2 of global fields (in preparation). · Zbl 0299.12013 [4] Birch, B. J.:K 2 of global fields (mimeographed proceedings of conference, S.U.N.Y. Stony Brook 1969). [5] Delzant, A.: Definition des classes de Stiefel-Whitney d’un module quadratique sur un corps de caractéristique différente de 2. C. R. Acad. Sci. Paris255, 1366-1368 (1962). · Zbl 0108.04303 [6] Kaplansky, I., Shaker, R. J.: Abstract quadratic forms. Canad. J. Math.21, 1218-1233 (1969). · Zbl 0238.15010 [7] Kervaire, M.: Multiplicateurs de Schur etK-théorie (to appear in de Rham Festschrift). [8] Matsumoto, H.: Sur les sous-groupes arithmétiques des groupes semi-simples deployés. Ann. Sci. Ec. Norm Sup. 4e série2, 1-62 (1969). · Zbl 0261.20025 [9] Milnor, J.: Notes on algebraicK-theory (to appear). [10] Moore, C.: Group extensions ofp-adic and adelic linear groups. Publ. Math. I.H.E.S.35, 5-74 (1969). [11] Nobile, A., Villamayor, O.: Sur laK-théorie algébrique. Ann. Sci. Ec. Norm. Sup. 4e série1, 581-616 (1968). · Zbl 0186.03101 [12] O’Meara, O. T.: Introduction to quadratic forms. Berlin-Göttingen-Heidelberg: Springer 1963. [13] Pfister, A.: Quadratische Formen in beliebigen Körpern. Inventiones math.1, 116-132 (1966). · Zbl 0142.27203 [14] Scharlau, W.: Quadratische Formen und Galois-Cohomologie. Inventiones math.4, 238-264 (1967). · Zbl 0165.35802 [15] Serre, J. P.: Cohomologie Galoisienne. Lecture Notes in Mathematics, Vol.5. Berlin-Heidelberg-New York: Springer 1964. · Zbl 0143.05901 [16] Springer, T. A.: Quadratic forms over a field with a discrete valuation. Indag. Math.17, 352-362 (1955). · Zbl 0067.27605 [17] Swan, R.: AlgebraicK-theory. Lecture Notes in Mathematics, Vol.76. Berlin-Heidelberg-New York: Springer 1968. · Zbl 0193.34601 [18] Swan, R.: Non-abelian homological algebra andK-theory, (mimeographed) Univ. of Chicago, 1968. [19] Tate, J.: Duality theorems in Galois cohomology over number fields. Proc. Int. Congr. Math. Stockholm, 288-295 (1963). · Zbl 0126.07002 [20] Weil, A.: Basic number theory. Berlin-Heidelberg-New York: Springer 1967. · Zbl 0176.33601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.