The de Jong fundamental group of a non-trivial abelian variety is non-abelian
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866908719678226432 |
|---|---|
| author | Howe, Sean |
| author_facet | Howe, Sean |
| contents | We show that the de Jong fundamental group of any non-trivial abelian variety over a complete algebraically closed extension $C/\mathbb{Q}_p$ is non-abelian. Generalizing an argument for $\mathbb{P}^1_C$, we also show that the de Jong fundamental group of any connected rigid analytic variety over $C$ admitting a non-constant map to $\mathbb{P}^n_C$ (e.g., an abelian variety) depends on $C$ and is big. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The de Jong fundamental group of a non-trivial abelian variety is non-abelian Howe, Sean Algebraic Geometry Number Theory We show that the de Jong fundamental group of any non-trivial abelian variety over a complete algebraically closed extension $C/\mathbb{Q}_p$ is non-abelian. Generalizing an argument for $\mathbb{P}^1_C$, we also show that the de Jong fundamental group of any connected rigid analytic variety over $C$ admitting a non-constant map to $\mathbb{P}^n_C$ (e.g., an abelian variety) depends on $C$ and is big. |
| title | The de Jong fundamental group of a non-trivial abelian variety is non-abelian |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2512.09661 |