Cdh descent, cdarc descent, and Milnor excision

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Dokumenter

  • Elden Elmanto
  • Marc Hoyois
  • Ryomei Iwasa
  • Shane Kelly

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 ∞-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.

OriginalsprogEngelsk
TidsskriftMathematische Annalen
Vol/bind379
Sider (fra-til)1011–1045
ISSN0025-5831
DOI
StatusUdgivet - 2021

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