The geometrically m-step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910829044039680 |
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| author | Yamaguchi, Naganori |
| author_facet | Yamaguchi, Naganori |
| contents | In this paper, we present some new results on the geometrically m-step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bi-anabelian and strong bi-anabelian) geometrically m-step solvable Grothendieck conjecture(s) for affine hyperbolic curves over fields finitely generated over the prime field. First of all, we show the conjecture over finite fields. Next, we show the geometrically m-step solvable version of the Oda-Tamagawa good reduction criterion for hyperbolic curves. Finally, by using these two results, we show the conjecture over fields finitely generated over the prime field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09253 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The geometrically m-step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields Yamaguchi, Naganori Algebraic Geometry In this paper, we present some new results on the geometrically m-step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bi-anabelian and strong bi-anabelian) geometrically m-step solvable Grothendieck conjecture(s) for affine hyperbolic curves over fields finitely generated over the prime field. First of all, we show the conjecture over finite fields. Next, we show the geometrically m-step solvable version of the Oda-Tamagawa good reduction criterion for hyperbolic curves. Finally, by using these two results, we show the conjecture over fields finitely generated over the prime field. |
| title | The geometrically m-step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2302.09253 |