Submission: 2010, Feb 17
The epicenter of this paper concerns Pfister quadratic forms over a field F with a Henselian discrete valuation. All characteristics are considered but we focus on the most complicated case where the residue field has characteristic 2 but F does not. We also prove results about round quadratic forms, composition algebras, generalizations of composition algebras we call conic algebras, and central simple associative symbol algebras. Finally we give relationships between these objects and Kato's filtration on the Milnor K-groups of F.
2000 Mathematics Subject Classification: Primary 17A75; secondary 11E04, 16W60, 17A45, 19D45, 19F15
Keywords and Phrases: Primary 17A75; secondary 11E04, 16W60, 17A45, 19D45, 19F15
Full text: dvi.gz 182 k, dvi 444 k, ps.gz 1015 k, pdf.gz 695 k, pdf 751 k.