Convergence of Voevodsky's slice tower

  • Marc Levine

    Universität Duisburg-Essen Fakultät Mathematik Campus Essen 45117 Essen Germany
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We consider Voevodsky's slice tower for a finite spectrum in the motivic stable homotopy category over a perfect field . In case has finite cohomological dimension, we show that the slice tower converges, in that the induced filtration on the bi-graded homotopy sheaves is finite, exhaustive and separated at each stalk (after inverting the exponential characteristic of ). This partially verifies a conjecture of Voevodsky.

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

DOI 10.4171/DM/416