detlev.hoffmann@nottingham.ac.uk
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
Full text: dvi.gz 18 k, dvi 39 k, ps.gz 617 k, pdf.gz 116 k, pdf 132 k.