Detlev W. Hoffmann: Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2

Submission: 2014, Mar 12

Let F be a field of characteristic 2 and let K/F be a purely inseparable extension of exponent 1. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed generators for the kernel W_q(K/F) of the natural restriction map W_q(F)\to W_q(K) between the Witt groups of quadratic forms of F and K, respectively, where K/F is a finite multiquadratic extension of separability degree at most 2.

2010 Mathematics Subject Classification: Primary 11E04; Secondary 11E81 12F15

Keywords and Phrases: Quadratic form, bilinear form, Pfister form, Witt group, excellent extension, purely inseparable extension, exponent of an inseparable extension

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