The Grothendieck-Witt group and Voevodsky's slice filtration

Morel has shown that the 0th homotopy group of the motivic sphere spectrum in the motivic stable homotopy category over a field k is the Grothendieck-Witt group of quadratic forms over k. Voevodsky has defined a motivic version of the classical Postnikov tower, which yields a refined version of Grothendieck's coniveau filtration. We relate these two by showing that the filtration on GW(k) induced by the motivic Postnikov tower is the same as the I-adic filtration, with I the augmentation ideal in GW(k). We examine as well the general question of convergence of the motivic Postnikov tower.