Continuité des racines d’après Rabinoff
The content of this paper is a generalization of a theorem by Joseph Rabinoff: if $\mathscr{P}$ is a finite family of pointed and rational 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 $\mathscr{P}$, if $k$ is a c...
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.439/ |
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| author | Marie, Emeryck |
| author_facet | Marie, Emeryck |
| author_sort | Marie, Emeryck |
| collection | DOAJ |
| description | The content of this paper is a generalization of a theorem by Joseph Rabinoff: if $\mathscr{P}$ is a finite family of pointed and rational 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 $\mathscr{P}$, if $k$ is a complete non-archimedean field, if $S$ is a connected and regular $k$-analytic space (in the sense of Berkovich) and $Y$ is a closed $k$-analytic subset of $U_{\mathscr{P}} \times _k S$ which is relative complete intersection and contained in the relative interior of $U_{\mathscr{P}} \times _k S$ over $S$, then the quasifiniteness of $\pi : Y \rightarrow S$ implies its flatness and finiteness; moreover, all the finite fibers of $\pi $ have the same length. This namely gives a analytic justification to the concept of stable intersection used in the theory of tropical intersection. |
| format | Article |
| id | doaj-art-65743d236d984662b726e552aebd8635 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-65743d236d984662b726e552aebd86352025-02-07T11:07:00ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-03-01361G368569610.5802/crmath.43910.5802/crmath.439Continuité des racines d’après RabinoffMarie, Emeryck0Technische Universität Chemnitz, Fakultät für Mathematik, Reichenhainer Straße 39, 09126 Chemnitz, GermanyThe content of this paper is a generalization of a theorem by Joseph Rabinoff: if $\mathscr{P}$ is a finite family of pointed and rational 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 $\mathscr{P}$, if $k$ is a complete non-archimedean field, if $S$ is a connected and regular $k$-analytic space (in the sense of Berkovich) and $Y$ is a closed $k$-analytic subset of $U_{\mathscr{P}} \times _k S$ which is relative complete intersection and contained in the relative interior of $U_{\mathscr{P}} \times _k S$ over $S$, then the quasifiniteness of $\pi : Y \rightarrow S$ implies its flatness and finiteness; moreover, all the finite fibers of $\pi $ have the same length. This namely gives a analytic justification to the concept of stable intersection used in the theory of tropical intersection.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.439/ |
| spellingShingle | Marie, Emeryck Continuité des racines d’après Rabinoff Comptes Rendus. Mathématique |
| title | Continuité des racines d’après Rabinoff |
| title_full | Continuité des racines d’après Rabinoff |
| title_fullStr | Continuité des racines d’après Rabinoff |
| title_full_unstemmed | Continuité des racines d’après Rabinoff |
| title_short | Continuité des racines d’après Rabinoff |
| title_sort | continuite des racines d apres rabinoff |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.439/ |
| work_keys_str_mv | AT marieemeryck continuitedesracinesdapresrabinoff |