Convergence of Voevodsky's slice tower

  • Marc Levine

    Universität Duisburg-Essen Fakultät Mathematik Campus Essen 45117 Essen Germany
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Abstract

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

Cite this article

Marc Levine, Convergence of Voevodsky's slice tower. Doc. Math. 18 (2013), pp. 907–941

DOI 10.4171/DM/416