Marc Levine

Grothendieck-Witt groups and convergence of the motivic Postnikov tower

Abstract.  Morel has computed the 0th homotopy group of the motivic sphere spectrum (in the motivic stable homotopy category SH(k) over a field k of characteristic not equal to 2) as the Grothendieck-Witt
group. We show that the filtration induced on this homotopy group by Voevodsky's slice tower is the I-adic filtration. In case the base has finite cohomological dimension and has characteristic zero, we show that the slice tower converges for all ``finite" spectra, that is, for those spectra in the thick triangulated subcategory of SH(k) generated by suspension spectra of smooth projective k-schemes and their (positive or negative) T-suspensions.