Excellence of function fields of conics

  • Alexander Merkurjev

    University of California, Los Angeles, USA
  • Jean-Pierre Tignol

    Université Catholique de Louvain, Belgium


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. 421–456

DOI 10.4171/LEM/62-3/4-3