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Cdh descent, cdarc descent, and Milnor excision

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arxiv 2002.11647 v3 pith:5BY344R5 submitted 2020-02-26 math.AG math.ATmath.KT

Elden Elmanto , Marc Hoyois , Ryomei Iwasa , Shane Kelly This is my paper · ORCID
classification math.AGmath.ATmath.KT
keywords excisionmilnordescentalongapplicationbhattcdarccohomology
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We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is hypercomplete, extending a theorem of Voevodsky to nonnoetherian schemes. As an application, we show that if E is a motivic spectrum over a field k which is n-torsion for some n invertible in k, then the cohomology theory on k-schemes defined by E satisfies Milnor excision.

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  1. Descendability and descent in topological weaves

    math.AG 2026-07 accept novelty 7.0 of 10

    Finitely presented surjections of algebraic spaces are descendable in topological weaves, yielding v-descent for rational motivic sheaves and h-descent for étale motivic spectra under bounded cohomological dimension.

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