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CANCELLED Milnor excision for motivic spectra

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KAHW02 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

Let k be a field and E a motivic spectrum over k which is n-torsion for some n invertible in k. We show that the cohomology theory on k-schemes defined by E satisfies Milnor excision. More generally, 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.




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