On \'etale motivic spectra and Voevodsky's convergence conjecture
K-Theory and Homology
2021-10-05 v3 Algebraic Topology
Abstract
We prove a new convergence result for the slice spectral sequence, following work by Levine and Voevodsky. This verifies a derived variant of Voevodsky's conjecture on convergence of the slice spectral sequence. This is, in turn, a necessary ingredient for our main theorem: a Thomason-style \'etale descent result for the Bott-inverted motivic sphere spectrum, which generalizes and extends previous \'etale descent results for special examples of motivic cohomology theories. Combined with first author's \'etale rigidity results, we obtain a complete structural description of the \'etale motivic stable category.
Keywords
Cite
@article{arxiv.2003.04006,
title = {On \'etale motivic spectra and Voevodsky's convergence conjecture},
author = {Tom Bachmann and Elden Elmanto and Paul Arne Østvær},
journal= {arXiv preprint arXiv:2003.04006},
year = {2021}
}
Comments
New title and introduction