Witt kernels and Brauer kernels for quartic extensions in characteristic two

摘要

Let F be a field of characteristic 2 and let El F be a field extension of degree 4. We determine the kernel W-q(E/F) of the restriction map WqF -> WqE between the Witt groups of nondegenerate quadratic forms over F and over E, completing earlier partial results by Ahmad, Baeza, Mammone and Moresi. We also deduce the corresponding result for the Witt kernel W(E/F) of the restriction map WF -> WE between the Witt rings of nondegenerate symmetric bilinear forms over F and over E from earlier results by the first author. As an application, we describe the 2-torsion part of the Brauer kernel for such extensions. (C) 2015 Elsevier B.V. All rights reserved.