Convergence of Voevodsky's slice tower
Algebraic Geometry
2013-03-08 v2 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1201.0279,
title = {Convergence of Voevodsky's slice tower},
author = {Marc Levine},
journal= {arXiv preprint arXiv:1201.0279},
year = {2013}
}
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