On the descent for quadratic and bilinear forms

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