Unstable motivic and real-étale homotopy theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915123202883584 |
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| author | Asok, Aravind Bachmann, Tom Elmanto, Elden Hopkins, Michael J. |
| author_facet | Asok, Aravind Bachmann, Tom Elmanto, Elden Hopkins, Michael J. |
| contents | We prove that for any base scheme $S$, real étale motivic (unstable) homotopy theory over $S$ coincides with unstable semialgebraic topology over $S$ (that is, sheaves of spaces on the real spectrum of $S$). Moreover we show that for pointed connected motivic spaces over $S$, the real étale motivic localization is given by smashing with the telescope of the map $ρ: S^0 \to {\mathbb G}_m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unstable motivic and real-étale homotopy theory Asok, Aravind Bachmann, Tom Elmanto, Elden Hopkins, Michael J. Algebraic Geometry Algebraic Topology K-Theory and Homology 14F42 14P10 55P60 We prove that for any base scheme $S$, real étale motivic (unstable) homotopy theory over $S$ coincides with unstable semialgebraic topology over $S$ (that is, sheaves of spaces on the real spectrum of $S$). Moreover we show that for pointed connected motivic spaces over $S$, the real étale motivic localization is given by smashing with the telescope of the map $ρ: S^0 \to {\mathbb G}_m$. |
| title | Unstable motivic and real-étale homotopy theory |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology 14F42 14P10 55P60 |
| url | https://arxiv.org/abs/2501.15651 |