On the real Section Conjecture in étale homotopy theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914094112571392 |
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| author | Holzschuh, Tim |
| author_facet | Holzschuh, Tim |
| contents | We study the Section Conjecture in étale homotopy theory for varieties over $\mathbb{R}$. We prove its pro-$2$ variant for equivariantly triangulable varieties. Examples include all smooth varieties as well as all (possibly singular) affine/projective varieties. Building on this, we derive the real Section Conjecture in the geometrically étale nilpotent (e.g. simply connected) case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the real Section Conjecture in étale homotopy theory Holzschuh, Tim Algebraic Geometry Algebraic Topology 14G05 (Primary) 14P25 (Secondary) We study the Section Conjecture in étale homotopy theory for varieties over $\mathbb{R}$. We prove its pro-$2$ variant for equivariantly triangulable varieties. Examples include all smooth varieties as well as all (possibly singular) affine/projective varieties. Building on this, we derive the real Section Conjecture in the geometrically étale nilpotent (e.g. simply connected) case. |
| title | On the real Section Conjecture in étale homotopy theory |
| topic | Algebraic Geometry Algebraic Topology 14G05 (Primary) 14P25 (Secondary) |
| url | https://arxiv.org/abs/2510.13325 |