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

TL;DR

This paper investigates Pfister quadratic forms over Henselian fields with a focus on complex cases involving characteristic 2 residue fields, exploring their connections with K-theory, conic algebras, and central simple algebras.

Contribution

It introduces new results on wild Pfister forms, conic algebras, and their relationships with Kato's filtration on Milnor K-groups in the context of Henselian fields.

Findings

Results on the structure of wild Pfister forms

Connections between conic algebras and K-theory

Relationships with Kato's filtration on Milnor K-groups

Abstract

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 $F$.