A number field analogue of the Grothendieck conjecture for curves over finite fields
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908469198585856 |
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| author | Ozaki, Manabu |
| author_facet | Ozaki, Manabu |
| contents | In the present paper, we provide a new analogy between number fields and 1-dimensional function fields over finite fields from the viewpoint that the maximal cyclotomic extension of a number field is analogous to the constant field extension of a function field to an algebraic closure. Namely, we give a number field analogue of the Grothendieck conjecture for hyperbolic curves over finite fields proved by Tamagawa and Mochizuki, which is an affirmative answer to Conjecture(12.5.3) of ``Cohomology of number fields" by Neukirch-Schmidt-Wingberg in the case where the ramified prime sets are empty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A number field analogue of the Grothendieck conjecture for curves over finite fields Ozaki, Manabu Number Theory In the present paper, we provide a new analogy between number fields and 1-dimensional function fields over finite fields from the viewpoint that the maximal cyclotomic extension of a number field is analogous to the constant field extension of a function field to an algebraic closure. Namely, we give a number field analogue of the Grothendieck conjecture for hyperbolic curves over finite fields proved by Tamagawa and Mochizuki, which is an affirmative answer to Conjecture(12.5.3) of ``Cohomology of number fields" by Neukirch-Schmidt-Wingberg in the case where the ramified prime sets are empty. |
| title | A number field analogue of the Grothendieck conjecture for curves over finite fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.20159 |