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arXiv · 1403.3064

Witt kernels and Brauer kernels for quartic extensions in characteristic two

Detlev W. Hoffmann·Marco Sobiech
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Abstract

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.

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Detlev W. Hoffmann, Marco Sobiech. 2014-03-12. Witt kernels and Brauer kernels for quartic extensions in characteristic two. https://arxiv.org/abs/1403.3064

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