  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.
