Mohamed Abdou Elomary and Jean-Pierre Tignol: Springer's theorem for tame quadratic forms over Henselian fields,

Submission: 2010, Feb 5

A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt group of graded quadratic forms over the graded ring associated to the filtration defined by the valuation, hence also isomorphic to a direct sum of copies of the Witt group of the residue field indexed by the value group modulo 2.

2000 Mathematics Subject Classification: 11E81

Keywords and Phrases: Henselian valuation, graded fields, residue quadratic forms

Full text: dvi.gz 33 k, dvi 77 k, ps.gz 729 k, pdf.gz 170 k, pdf 192 k.

Server Home Page