On schemes with trivial higher étale homotopy groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910033179049984 |
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| author | Moutand, Mohammed |
| author_facet | Moutand, Mohammed |
| contents | Let $(X,\bar x)$ be a pointed connected noetherian scheme. In this note, we give characterizations for the vanishing of the second étale homotopy group $π^{\rm ét}_2(X,\bar x)$ in terms of splitting profinite-étale covers of $X$, and by means of universal covering spaces of the Artin-Mazur-Friedlander étale homotopy type $Et(X)$. In particular, this provides certain classes of schemes for which the Brauer map is surjective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08505 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On schemes with trivial higher étale homotopy groups Moutand, Mohammed Algebraic Geometry Let $(X,\bar x)$ be a pointed connected noetherian scheme. In this note, we give characterizations for the vanishing of the second étale homotopy group $π^{\rm ét}_2(X,\bar x)$ in terms of splitting profinite-étale covers of $X$, and by means of universal covering spaces of the Artin-Mazur-Friedlander étale homotopy type $Et(X)$. In particular, this provides certain classes of schemes for which the Brauer map is surjective. |
| title | On schemes with trivial higher étale homotopy groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.08505 |