Cdh descent, cdarc descent, and Milnor excision
| Autor: | Elden Elmanto, Marc Hoyois, Shane Kelly, Ryomei Iwasa |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
General Mathematics Dimension (graph theory) Field (mathematics) Mathematics::Algebraic Topology 01 natural sciences Spectrum (topology) law.invention Mathematics - Algebraic Geometry Mathematics::K-Theory and Homology law 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Algebraic Geometry (math.AG) Descent (mathematics) Mathematics 010102 general mathematics K-Theory and Homology (math.KT) Cohomology Invertible matrix Scheme (mathematics) Mathematics - K-Theory and Homology Sheaf 010307 mathematical physics |
| Zdroj: | Elmanto, E, Hoyois, M, Iwasa, R & Kelly, S 2021, ' Cdh descent, cdarc descent, and Milnor excision ', Mathematische Annalen, vol. 379, pp. 1011–1045 . https://doi.org/10.1007/s00208-020-02083-5 |
| ISSN: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s00208-020-02083-5 |
| Popis: | 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. Comment: 28 pages. v3: final version, to appear in Mathematische Annalen; v2: new title and minor corrections |
| Databáze: | OpenAIRE |
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