Detlev W. Hoffmann: Witt kernels of bilinear forms for algebraic extensions in characteristic 2

Submission: 2004, Oct 11

Let F be a field of characteristic 2 and let K/F be a purely inseparable extension of exponent 1. We determine the kernel W(K/F) of the natural restriction map from WF to WK between the Witt rings of bilinear forms of F and K, respectively. This complements a result by Laghribi who computed the kernel for the Witt groups of quadratic forms for such an extension K/F. Based on this result, we will determine W(K/F) for a wide class of finite extensions which are not necessarily purely inseparable.

2000 Mathematics Subject Classification: Primary 11E04; Secondary 11E81 12F15

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

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