On quadratic forms isotropic over the function field of a conic

by Markus Rost (3 pages)

Math. Ann. 288 (1990), no. 3, 511-513.

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.

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Related:

Hoffmann, Detlev W.; Laghribi, Ahmed. Isotropy of quadratic forms over the function field of a quadric in characteristic 2. J. Algebra 295 (2006), no. 2, 362-386. MR 2194958, Zbl 1138.11012.
Laghribi, Ahmed; Mukhija, Diksha. The excellence of function fields of conics. Proc. Amer. Math. Soc. 152 (2024), no. 5, 1915-1923. MR 4728462, Zbl 1554.11032.