Cdh descent, cdarc descent, and Milnor excision
Algebraic Geometry
2020-10-02 v3 Algebraic Topology
K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.2002.11647,
title = {Cdh descent, cdarc descent, and Milnor excision},
author = {Elden Elmanto and Marc Hoyois and Ryomei Iwasa and Shane Kelly},
journal= {arXiv preprint arXiv:2002.11647},
year = {2020}
}
Comments
28 pages. v3: final version, to appear in Mathematische Annalen; v2: new title and minor corrections