Convergence of Voevodsky's slice tower, by Marc Levine

We consider Voevodsky's slice tower for a finite spectrum E in the motivic stable homotopy category SH(k) over a perfect field k. In case k has finite cohomological dimension (in characteristic two, we also require that k is infinite), we show that the slice tower converges, in that the induced filtration on the bi-graded homotopy sheaves πa,bfnE of the nth term in the slice tower is finite, exhaustive and separated at each stalk. This partially verifies a conjecture of Voevodsky.

Marc Levine <>