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arXiv · 1901.00789

Arason's filtration of the Witt group of dyadic valued fields

Joachim Verstraete
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Abstract

Generalizing a theorem of Springer, we construct an extended Arason filtration by subgroups for the Witt group of quadratic forms of a general valued field, relating these subgroups with Witt-like groups of the residue field, in arbitrary characteristic. These Witt-like groups involve totally singular quadratic forms. In the case of a discretely valued field, we recover the original Arason filtration.

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Joachim Verstraete. 2019-01-03. Arason's filtration of the Witt group of dyadic valued fields. https://doi.org/10.1016/j.jalgebra.2018.10.026

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