Springer's theorem for tame quadratic forms over Henselian fields

Details Springer's theorem for tame quadratic forms over Henselian fields Springer's theorem for tame quadratic forms over Henselian fields

2010-02-05

arxiv.org/abs/1002.1153v1

Mathematics

K-Theory and Homology

Scientific paper

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.

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