Marc Levine
Published 2011-12-31, updated 2013-03-07Version 2
We consider Voevodsky's slice tower for a finite spectrum E in the motivic stable homotopy category 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 for each term in the tower for E is finite, exhaustive and separated at each stalk. This partially verifies a conjecture of Voevodsky.
Comments: revised version. Arguments simplified, bounds are improved and made explicit, some technical hypotheses removed. An appendix on inverting integers in triangulated categories is added
Smooth motives
Quotients of MGL, their slices and their geometric parts
A comparison of motivic and classical homotopy theories
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