Pacific Journal of Mathematics

Quadratic forms over dyadic valued fields. I. The graded Witt ring.

Bill Jacob

Article information

Pacific J. Math., Volume 126, Number 1 (1987), 21-79.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
Secondary: 12J10: Valued fields 13J15: Henselian rings [See also 13B40] 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 19G12: Witt groups of rings [See also 11E81]


Jacob, Bill. Quadratic forms over dyadic valued fields. I. The graded Witt ring. Pacific J. Math. 126 (1987), no. 1, 21--79.

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  • [D] A. Dress, Metrische Ebenen ber quadraisch perfecten Kbrpern, Math. Zeit, 92 (1965), 19-29.
  • [ELTW] R. Elman, T. Y. Lam, J.-P. Tignol and A. Wadsworth, Witt rings and Brauer groups under multiquadratic extensions I, Amer. J. Math., 105 (1983), 1119-1170.
  • [ELW1] R. Elman, T. Y. Lam and A. Wadsworth, Amenable fields and Pfister extensions, Proc. of Quadratic Forms Conference, 1976, (ed. G. Orzech) 445-492, Queens Papers in Pure and Applied Math. 46, Queens University, Kingston, Ontario.
  • [ELW2] R. Elman, Quadratic forms under multiquadratic extensions, Indag. Math., 42 (1980), 131-145.
  • [G] M. Greenberg, Lectures on Forms in Many Variables, W. A. Benjamin Inc., 1969.
  • [Kl] K. Kato, Galois Cohomology of Complete Discrete Valued Fields, in Proceed- ings of June Oberwolfach Conference on Algebraic J-Theory, Springer Lec- ture Notes #966 (1982).
  • [K2] K. Kato, Symmetric bilinear forms and Milnor K-theory in characteristic 2, Inventions Math., 66 (1982),493-512.
  • [Kn] M. Knebusch, Generic theory of quadraticforms I, Proc. London Math. So, 33 (1977), 65-93, Part II, ibid,34 (1977), 1-31.
  • [Kn-Sc] M. Knebusch and W. Scharlau, Algebraic Theory of Quadratic Forms: Generic Methods and Pfister Forms, D. M. V. Seminar # 1 , Birkhauser, Boston, 1980.
  • [Ku] M. Kula, Fields with prescribed quadratic form schemes, Math. Zeit., 167 (1979), 201-212.
  • [L] T. Y. Lam, Algebraic Theory of Quadratic Forms, W. A. Benjamin Inc., (1973).
  • [M] M. Marshall, Abstract Witt Rings, Queen's Papers in Pure and Applied Mathematics #57,Kingston, Ontario, (1980).
  • [Ml] J. Milnor, Algebraic K-Theory and quadraticforms, Invent. Math., 9 (1970), 318-344.
  • [M2] J. Milnor, Symmetric inner products in characteristic 2, Prospects in Math, Annals of Math Studies, Princeton University Press (1971), 59-75.
  • [Me] A. Merkurjev, On the norm residue symbol of degree 2, Soviet Math. Doklady, 24 (1981), 546-551.
  • [STW] D. Shapiro, J. Tignol and A. Wadsworth, Witt Rings and Brauer groups under multiquadratic extensions II,J. Algebra, 78 (1982), 58-90.
  • [S] T. A. Springer, Quadratic forms over fields with a discrete valuation, Indag. Math., 17 (1955), 352-362.
  • [T] U. P. Tietze, Zur Theorie quadratischer Formen iber Hensel-Korpern, Arch. Math., 25 (1974), 144-150.
  • [W] A. Wadsworth, p-Henselian fields: K-theory, Galois cohomology, and graded Witt rings, Pacific J. Math., 105 (1983), 473-496.

See also

  • Bill Jacob. Quadratic forms over dyadic valued fields. {II}. Relative rigidity and Galois cohomology. II [MR 93d:11045] J. Algebra 148 1992 1 162--202.