References
[A1] Arason, J.K.: Cohomologische Invarianten Quadratischer Formen. J. Algebra36, 448–491 (1975)
[A2] Arason, J.K.: A Proof of Merkurjev's Theorem; Can. Math. Soc. Conf. Proc.4, 121–130 (1984)
[AEJ1] Arason, J.K., Elman, R., Jacob, B.: Fields of cohomological 2-dimension three. Math. Ann.274, 649–657 (1986)
[AEJ2] Arason, J.K., Elman, R., Jacob, B.: On quadratic forms and Galois cohomology. Proceedings of the 1986 Corvallis Conference. Rocky Mt. J. Math. (1989) to appear
[EL] Elman, R., Lam, T.-Y.: Pfister forms andK-theory of fields. J. Algebra23, 181–213 (1972)
[G] Grayson, D.R.: Localization for flat modules in algebraicK-theory. J. Algebra61, 463–496 (1979)
[K] Kato, K.: MilnorK-theory and the Chow group of zero cycles. Contemp. Math.55, 241–253 (1986)
[L] Lam, T.Y.: The algebraic theory of quadratic forms. New York: Benjamin 1973
[Me] Merkurjev, A.S.: On the norm residue symbol of degree 2. Dokl. Akad. Nauk. SSSR261, 542–547 (1981); (English Translatio) Sov. Math., Dokl.24, 546–551 (1981)
[MSt] Merkurjev, A.S., Suslin, A.A.: Ontthe norm residue homomorphism of degree three. LOMI preprint (1986)
[MS2] Merkurjev, A.S., Suslin, A.A.: On theK 3 of a field. LOMI preprint (1986)
[Mi] Milnor, J.: AlgebraicK-theory and quadratic forms. Invent. Math.9, 318–344 (1970)
[Q] Quillen, D.: Higher algebraicK-theory, I. (Lecture Notes Math, Vol. 341, pp. 77–139). Berlin-Heidelberg-New York: Springer 1973
[R1] Rost, M.:SK 1 of some non-singular quadrics, research announcement (1986)
[R2] Rost, M.: Injectivity ofK 2 D→K 2 F for quaternion algebras. Preprint (1986)
[R3] Rost, M.: Hilbert 90 forK 3 for degree-two extensions. Preprint (1986)
[Sc] Scharlau, W.: Quadratic and hermitian forms. Berlin-Heidelberg-New York: Springer 1985
[Sh1] Sherman, C.: Some theorems on theK-theory of coherent sheaves. Commun. Algebra7, 1489–1508 (1979)
[Sh2] Sherman, C.:K-theory of regular schemes. Commun. Algebra7, 999–1027 (1979)
[Su1] Suslin, A.A.: Quaternion homomorphism for the function field of a conic. Dokl. Akad. Nauk. SSSR265, 292–296 (1982); (English Translation) Sov. Math. Dokl.26, 72–77 (1982)
[Su2] Suslin, A.A.: Torsion inK 2 of Fields. J.K-theory1, 5–29 (1987)
[Sw] Swan, R.:K-theory of Quadric Hypersurfaces. Ann. Math.112, 113–153 (1985)
[W] Wadsworth, A.R.: Merkurjev's Elementary proof of Merkurjev's Theorem. Contemp. Math.55, 741–776 (1986)
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Professor Jacob gratefuly acknowledges the Mathematical Sciences Research Institute, Berkeley California, for its support and excellent working conditions provided during 1986–1987. Additional support was provided by the National Science Foundation and the Research Office of Oregon State University
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Jacob, B., Rost, M. Degree four cohomological invariants for quadratic forms. Invent Math 96, 551–570 (1989). https://doi.org/10.1007/BF01393696
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DOI: https://doi.org/10.1007/BF01393696