The de Jong fundamental group of $\mathbb{P}^1_C$ depends on $C$ and is not always topologically countably generated
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917153082441728 |
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| author | Howe, Sean |
| author_facet | Howe, Sean |
| contents | For $C/\mathbb{Q}_p$ complete and algebraically closed, we show that the de Jong fundamental group $π_{1,\mathrm{dJ}}(\mathbb{P}^1_C)$ depends on $C$ and, if $C$ has cardinality $>2^{\mathbb{N}}$, that it is not topologically countably generated. The result and proofs generalize to any connected rigid analytic variety with a non-constant map to $\mathbb{P}^n_C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The de Jong fundamental group of $\mathbb{P}^1_C$ depends on $C$ and is not always topologically countably generated Howe, Sean Algebraic Geometry Number Theory For $C/\mathbb{Q}_p$ complete and algebraically closed, we show that the de Jong fundamental group $π_{1,\mathrm{dJ}}(\mathbb{P}^1_C)$ depends on $C$ and, if $C$ has cardinality $>2^{\mathbb{N}}$, that it is not topologically countably generated. The result and proofs generalize to any connected rigid analytic variety with a non-constant map to $\mathbb{P}^n_C$. |
| title | The de Jong fundamental group of $\mathbb{P}^1_C$ depends on $C$ and is not always topologically countably generated |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2512.09651 |