### 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 π_{a,b}f_{n}E
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 <marc.levine@uni-due.de>