Cdh descent, cdarc descent, and Milnor excision
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- CDH DESCENT, CDARC DESCENT, AND MILNOR EXCISION
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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 ∞-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.
Originalsprog | Engelsk |
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Tidsskrift | Mathematische Annalen |
Vol/bind | 379 |
Sider (fra-til) | 1011–1045 |
ISSN | 0025-5831 |
DOI | |
Status | Udgivet - 2021 |
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