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Cycles for rational maps of good reduction outside a prescribed set

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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Official URL: http://edoc.unibas.ch/51690/

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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)
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
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Last Modified:27 Nov 2017 12:59
Deposited On:27 Nov 2017 12:59

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