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arXiv · 2003.04006

On étale motivic spectra and Voevodsky's convergence conjecture

Tom Bachmann·Elden Elmanto·Paul Arne Østvær
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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 étale descent result for the Bott-inverted motivic sphere spectrum, which generalizes and extends previous étale descent results for special examples of motivic cohomology theories. Combined with first author's étale rigidity results, we obtain a complete structural description of the étale motivic stable category.

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Tom Bachmann, Elden Elmanto, Paul Arne Østvær. 2021-10-04. On étale motivic spectra and Voevodsky's convergence conjecture. https://arxiv.org/abs/2003.04006

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