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

## TL;DR

This paper extends Arason's filtration to the Witt group of quadratic forms over general valued fields, linking it with Witt-like groups of the residue field, including totally singular forms, and recovers the classical case for discretely valued fields.

## Contribution

It generalizes Arason's filtration to arbitrary valued fields and relates it to Witt-like groups of the residue field, including totally singular quadratic forms.

## Key findings

- Constructed an extended Arason filtration for general valued fields.
- Connected the filtration subgroups with Witt-like groups of the residue field.
- Recovered the classical Arason filtration in the discretely valued case.

## 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.