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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2407.09906 |
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| _version_ | 1866916322600812544 |
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| author | Yamaguchi, Naganori |
| author_facet | Yamaguchi, Naganori |
| contents | In the present paper, we show a new result on the geometrically $2$-step solvable Grothendieck conjecture for genus $0$ curves over finitely generated fields. More precisely, we show that two genus $0$ hyperbolic curves over a finitely generated field $k$ are isomorphic as $k$-schemes (up to Frobenius twists) if and only if the geometrically maximal $2$-step solvable quotients of their étale fundamental groups are isomorphic as topological groups over the absolute Galois group of $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A refined version of the geometrically m-step solvable Grothendieck conjecture for genus 0 curves over finitely generated fields Yamaguchi, Naganori Algebraic Geometry In the present paper, we show a new result on the geometrically $2$-step solvable Grothendieck conjecture for genus $0$ curves over finitely generated fields. More precisely, we show that two genus $0$ hyperbolic curves over a finitely generated field $k$ are isomorphic as $k$-schemes (up to Frobenius twists) if and only if the geometrically maximal $2$-step solvable quotients of their étale fundamental groups are isomorphic as topological groups over the absolute Galois group of $k$. |
| title | A refined version of the geometrically m-step solvable Grothendieck conjecture for genus 0 curves over finitely generated fields |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.09906 |