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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2108.11214 |
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| _version_ | 1866914044898705408 |
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| author | Marie, Emeryck |
| author_facet | Marie, Emeryck |
| contents | The content of this paper is a generalization of a the theorem 9.2 of the paper arXiv:1007.2665 written by Joseph Rabinoff : if $\mathcal{P}$ is a finite family of polyhedra in $N_{\mathbb{R}}$ such that there exists a fan in $N_{\mathbb{R}}$ that contains all the recession cones of the polyhedra of $\mathcal{P}$, if $k$ is a complete non-archimedean field, if $S$ is a connected and regular $k$-analytic space and $Y$ is a closed $k$-analytic subset of $U_{\mathcal{P}} \times_k S$ which is relative complete intersection and contained in the relative interior of $U_{\mathcal{P}} \times_k S$ over $S$, then the quasifiniteness of $π: Y \to S$ implies its flatness and its finiteness ; moreover, all the finite fibres of $π$ have the same cardinality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_11214 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Continuité des racines d'après Rabinoff et Berkovich Marie, Emeryck Algebraic Geometry 13, 14, 51, 52 The content of this paper is a generalization of a the theorem 9.2 of the paper arXiv:1007.2665 written by Joseph Rabinoff : if $\mathcal{P}$ is a finite family of polyhedra in $N_{\mathbb{R}}$ such that there exists a fan in $N_{\mathbb{R}}$ that contains all the recession cones of the polyhedra of $\mathcal{P}$, if $k$ is a complete non-archimedean field, if $S$ is a connected and regular $k$-analytic space and $Y$ is a closed $k$-analytic subset of $U_{\mathcal{P}} \times_k S$ which is relative complete intersection and contained in the relative interior of $U_{\mathcal{P}} \times_k S$ over $S$, then the quasifiniteness of $π: Y \to S$ implies its flatness and its finiteness ; moreover, all the finite fibres of $π$ have the same cardinality. |
| title | Continuité des racines d'après Rabinoff et Berkovich |
| topic | Algebraic Geometry 13, 14, 51, 52 |
| url | https://arxiv.org/abs/2108.11214 |