Geodesic
Convergence of Voevodsky's slice tower
Documenta mathematica, Tome 18 (2013), pp. 907-941
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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, we show that the slice tower converges, in that the induced filtration on the bi-graded homotopy sheaves Πa,b​fn​E is finite, exhaustive and separated at each stalk (after inverting the exponential characteristic of k). This partially verifies a conjecture of Voevodsky.
DOI : 10.4171/dm/416
Classification : 14F42, 55P42
Mots-clés : motivic homotopy theory, slice filtration, Morel-Voevodsky stable homotopy category 
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     author = {Marc Levine},
     title = {Convergence of {Voevodsky's} slice tower},
     journal = {Documenta mathematica},
     pages = {907--941},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/416},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/416/}
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Marc Levine. Convergence of Voevodsky's slice tower. Documenta mathematica, Tome 18 (2013), pp. 907-941. doi: 10.4171/dm/416

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