ON THE DESCENT FOR QUADRATIC AND BILINEAR FORMS

Ahmed Laghribi (1) , Diksha Mukhija (1)

1 LML - Laboratoire de Mathématiques de Lens

This paper is devoted to the study of the descent problem in the spirit of conjectures proposed by Kahn in characteristic different from 2 [15]. Descent problem seeks conditions under which a K-form (quadratic or bilinear) is defined over F for a field extension K/F. We study this problem in a complete manner for K-quadratic and bilinear forms up to dimension 4 when F is a field of characteristic 2 and K is the function field of a projective quadric.

Keywords: Quadratic (bilinear) form; Function field of a quadric; Descent; Witt kernel

Domains: Mathematics [math]; Commutative Algebra [math.AC]; Rings and Algebras [math.RA]

Ahmed Laghribi, Diksha Mukhija. ON THE DESCENT FOR QUADRATIC AND BILINEAR FORMS. 2023. ⟨hal-04084290⟩