For every generalized quadratic form or hermitian form over a division algebra, the anisotropic kernel of the form obtained by scalar extension to the function field of a smooth projective conic is defined over the field of constants. Tjhe proof does not require any hypothesis on the characteristic.
Cite this article
Alexander Merkurjev, Jean-Pierre Tignol, Excellence of function fields of conics. Enseign. Math. 62 (2016), no. 3/4, pp. 421–456DOI 10.4171/LEM/62-3/4-3