Submission: 2014, Mar 12
Let F be a field of characteristic 2 and let E/F be a field extension of degree 4. We determine the kernel W_q(E/F) of the restriction map W_qF\to W_qE 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 deduct the corresponding result for the Witt kernel W(E/F) of the restriction map WF\to WE between the Witt rings of nondegenerate symmetric bilinear forms over F and over E from earlier results by the first author. As application, we describe the 2-torsion part of the Brauer kernel for such extensions.
2010 Mathematics Subject Classification: Primary 11E04; Secondary 11E81 12F05 16K50
Keywords and Phrases: quartic extension, quadratic form, bilinear form, Witt group, Witt ring, Witt kernel, Brauer group, quaternion algebra, biquaternion algebra
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