Springer's theorem for tame quadratic forms over Henselian fields

Elomary, Mohamed Abdou;Tignol, Jean-Pierre
(2011) Mathematische Zeitschrift — Vol. 269, n° 1, p. 309-323 (2011)

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Abstract
A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tame 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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Elomary, M. A., & Tignol, J.-P. (2011). Springer’s theorem for tame quadratic forms over Henselian fields. Mathematische Zeitschrift, 269(1), 309-323. https://doi.org/10.1007/s00209-010-0729-y (Original work published 2011)