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On quadratic forms isotropic over the function field of a conic. (English) Zbl 0698.12009

This note contains a short proof of the fact that the function field of a curve of genus 0 is excellent in the sense of quadratic form theory.
Reviewer: M.Rost

MSC:

11R58 Arithmetic theory of algebraic function fields
11E12 Quadratic forms over global rings and fields
14H05 Algebraic functions and function fields in algebraic geometry
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References:

[1] Arason, J.Kr.: Cohomologische Invarianten quadratischer Formen. J. Algebra36, 448-491 (1975) · Zbl 0314.12104 · doi:10.1016/0021-8693(75)90145-3
[2] Elman, R., Lam, T.Y., Wadsworth, A.R.: Amenable fields and Pfister extensions. Conference on quadratic forms 1976. Queen’s pap. Pure Appl. Math.46, 445-491 (1977)
[3] Lam, T.Y.: Fields ofu-invariant 6 after A. Merkuriev. In: ?Ring theory 1989? in honour of S. A. Amitsur. Isr. Conf. Proc., vol. 1, pp. 12-30
[4] Scharlau, W.: Quadratic and hermitian forms. Berlin Heidelberg New York: Springer (1985) · Zbl 0584.10010
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