Convergence of voevodsky's slice tower

Abstract

We consider Voevodsky's slice tower for a finite spectrum ε in the motivic stable homotopy category over a perfect field k. In case k has finite cohomological dimension, we show that the slice tower converges, in that the induced filtration on the bi-graded homotopy sheaves Πa,bfnε is finite, exhaustive and separated at each stalk (after inverting the exponential characteristic of k). This partially verifies a conjecture of Voevodsky.