Wild Pfister forms over Henselian fields, K-theory, and conic division algebras

Details Wild Pfister forms over Henselian fields, K-theory, and conic division algebras Wild Pfister forms over Henselian fields, K-theory, and conic division algebras

2010-02-17

arxiv.org/abs/1002.3280v1

Journal of Algebra 327 #1 (2011), 386-465

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.jalgebra.2010.07.039

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 $F$.

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