Abstract

Let F be a field of characteristic 2 and let E/F be a field extension of degree 4. We determine the kernel Wq(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.

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