Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909197346537472 |
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| author | Bresciani, Giulio |
| author_facet | Bresciani, Giulio |
| contents | J. Silverman proved that a dynamical system on $\mathbb{P}^{1}$ descends to the field of moduli if it is polynomial or it has even degree, but for non-polynomial ones of odd degree the picture is less clear. We give a complete characterization of which dynamical systems over $\mathbb{P}^{1}$ descend to the field of moduli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman Bresciani, Giulio Number Theory Algebraic Geometry Dynamical Systems J. Silverman proved that a dynamical system on $\mathbb{P}^{1}$ descends to the field of moduli if it is polynomial or it has even degree, but for non-polynomial ones of odd degree the picture is less clear. We give a complete characterization of which dynamical systems over $\mathbb{P}^{1}$ descend to the field of moduli. |
| title | Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman |
| topic | Number Theory Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2405.03612 |