Quadratic forms over dyadic valued fields. I. The graded Witt ring

William B. Jacob

Vol. 126 (1987), No. 1, 21–79

DOI: 10.2140/pjm.1987.126.21

Abstract

This paper gives a detailed account of the arithmetic of quadratic forms over a field F of characteristic 0, carrying a 2-Henselian discrete valuation with residue field of characteristic 2. We give an analogue of Springer’s Theorem for the graded Witt ring of such a field, and describe new counterexamples to the amenability problem for multiquadratic extensions. The sequel to this paper will contain an axiomatic approach to the results contained herein, and will treat the Galois cohomology of such fields.

Mathematical Subject Classification 2000

Primary: 11E81

Secondary: 12J10, 13J15, 18F25, 19G12

Milestones

Received: 23 April 1984

Revised: 2 October 1985

Published: 1 January 1987