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# 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.

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