English

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