Canci, Jung Kyu.
(2006)
* Cycles for rational maps of good reduction outside a prescribed set.*
Monatshefte für Mathematik, 149 (4).
pp. 265-287.

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## Abstract

Let K be a number field and S a fixed finite set of places of K containing all the archimedean ones. Let RS be the ring of S-integers of K. In the present paper we study the cycles in P1(K) for rational maps of degree ≥2 with good reduction outside S. We say that two ordered n-tuples (P0, P1,… ,Pn−1) and (Q0, Q1,… ,Qn−1) of points of P1(K) are equivalent if there exists an automorphism A ∈ PGL2(RS) such that Pi = A(Qi) for every index i∈{0,1,… ,n−1}. We prove that if we fix two points P0,P1∈P1(K), then the number of inequivalent cycles for rational maps of degree ≥2 with good reduction outside S which admit P0, P1 as consecutive points is finite and depends only on S and K. We also prove that this result is in a sense best possible.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger) |
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UniBasel Contributors: | Canci, Jung Kyu |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Springer |

ISSN: | 0026-9255 |

e-ISSN: | 1436-5081 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Identification Number: | |

Last Modified: | 27 Nov 2017 12:59 |

Deposited On: | 27 Nov 2017 12:59 |

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