Canci, Jung Kyu.
(2015)
* Good reduction for endomorphisms of the projective line in terms of the branch locus.*
Preprints Fachbereich Mathematik, 2015 (36).

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## Abstract

Let K be a number field and v a non archimedean valuation on K. We say that an endomorphism $\Phi:\mathbb{P}_1 \to \mathbb{P}_1$ has good reduction at v if there exists a model $\Psi$ for $\Phi$ such that $deg \Psi_v$, the degree of the reduction of $\Psi$ modulo v, equals $deg \Psi$ and $\Psi_v$ is separable. We prove a criterion for good reduction that is the natural generalization of a result due to Zannier in [Z3]. Our result is in connection with other two notions of good reduction, the simple and the critically good reduction. The last part of our article is dedicated to prove a characterization of the maps whose iterates, in a certain sense, preserve the critically good reduction.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger) 12 Special Collections > Preprints Fachbereich Mathematik |
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UniBasel Contributors: | Canci, Jung Kyu |

Item Type: | Preprint |

Publisher: | Universität Basel |

Language: | English |

Last Modified: | 07 May 2019 15:23 |

Deposited On: | 28 Mar 2019 09:51 |

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