Witt kernels and Brauer kernels for quartic extensions in characteristic two

2014/03/12 by Detlev W. Hoffmann, Hoffmann, Detlev W., Marco Sobiech +1
Mathematics · #11E04 (primary) 11E81 12F05 16K50 (secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:11E04 #msc:11E81 #msc:12F05 #msc:16K50

paper · pdf · doi:10.48550/arxiv.1403.3064

arxiv created 2014/03/12 · arxiv updated 2014/03/13

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→ 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→ 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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