Abstract
We consider Voevodsky's slice tower for a finite spectrum \mathcal E 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 \Pi_{a,b}f_n\mathcal E is finite, exhaustive and separated at each stalk (after inverting the exponential characteristic of k ). This partially verifies a conjecture of Voevodsky.
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