The Uniform Boundedness and Dynamical Lang Conjectures for polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914211175596032 |
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| author | Looper, Nicole R. |
| author_facet | Looper, Nicole R. |
| contents | We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical analogue of Lang's conjecture on minimal canonical heights for these maps. We obtain similar results for non-isotrivial polynomials over a function field of characteristic zero. When the latter are unicritical of degree at least 5, the results hold unconditionally. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05240 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Uniform Boundedness and Dynamical Lang Conjectures for polynomials Looper, Nicole R. Number Theory Dynamical Systems 11G50, 11J97, 37P15, 37P35 We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical analogue of Lang's conjecture on minimal canonical heights for these maps. We obtain similar results for non-isotrivial polynomials over a function field of characteristic zero. When the latter are unicritical of degree at least 5, the results hold unconditionally. |
| title | The Uniform Boundedness and Dynamical Lang Conjectures for polynomials |
| topic | Number Theory Dynamical Systems 11G50, 11J97, 37P15, 37P35 |
| url | https://arxiv.org/abs/2105.05240 |