Cubic points on dynamical modular curves
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915618893070336 |
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| author | Doyle, John R. Galarraga, Alexander |
| author_facet | Doyle, John R. Galarraga, Alexander |
| contents | We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use this to prove a classification statement on preperiodic points for quadratic polynomials over cubic fields, extending previous work of Poonen, Faber, and the first author and Krumm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cubic points on dynamical modular curves Doyle, John R. Galarraga, Alexander Number Theory Algebraic Geometry Dynamical Systems 37P15, 37P35 (Primary) 11G30, 14G05 (Secondary) We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use this to prove a classification statement on preperiodic points for quadratic polynomials over cubic fields, extending previous work of Poonen, Faber, and the first author and Krumm. |
| title | Cubic points on dynamical modular curves |
| topic | Number Theory Algebraic Geometry Dynamical Systems 37P15, 37P35 (Primary) 11G30, 14G05 (Secondary) |
| url | https://arxiv.org/abs/2511.11491 |