Submission: 2003, Oct 14
For a nonreal field F of characteristic different from 2, we compare several properties which F may have with respect to an anisotropic n-fold Pfister form p over F. In particular, we consider the situation where the subforms of p are all the anisotropic quadratic forms over F; then p is said to be supreme. We further apply our results to the case where p is the form <1,...,1>. In this way we obtain new examples of nonreal fields with prescribed level and with additional properties.
2000 Mathematics Subject Classification: 11E25, 11E81, 16K50, 19D45
Keywords and Phrases: Pfister form, local field, Hilbert symbol, nonreal field, level, symbol length
Full text: dvi.gz 47 k, dvi 120 k, ps.gz 700 k, pdf.gz 242 k, pdf 284 k.