2011/12/31 by Marc Levine, Levine, Marc
Mathematics · #14C25 #19E15 (Primary) 19E08 14F42 #55P42 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14C25 #msc:14F42 #msc:19E08 #msc:19E15 #msc:55P42
paper · pdf · doi:10.48550/arxiv.1201.0279
revised version. Arguments simplified, bounds are improved and made explicit, some technical hypotheses removed. An appendix on inverting integers in triangulated categories is added
openalex publication_date 2011/12/31 · arxiv created 2013/03/07 · arxiv updated 2013/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.