Supreme Pfister Forms

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Nokhodkar Hassan Abadi, Amir Hossein | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39738 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
In this thesis we investigate the consept of supreme Pfister forms developed by K. J. Becher. Let F be a field of characteristic different from 2. Several properties of F with respect to an anisotropic form ϕ over F are introduced and their relations are studied. A form ϕ is called supreme if it is anisotropic and every anisotropic form over F is a subform of ϕ. It can be easily shown that if F has a supreme form then F is nonreal and ϕ is a Pfister form. We see how examples of such fields may be obtained. Also we compare fields having a supreme Pfister form with n-local fields (i.e., fields which up to isometry have exactly two n-fold Pfister forms). Finally, we apply our results to the case where ϕ is the form n× < > (n ≥ ).
Keywords:
Henslian Valuation ; Supreme Form ; 2-Maximal Field ; N-Local Field ; N-Hilbert Field ; Level Form

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