Étale motivic spectra and Voevodsky’s convergence conjecture
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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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Journal of the European Mathematical Society, 27, 7, EMS, Paris, 2025, https://doi.org/10.4171/jems/1421