Rational periodic points for quadratic maps

Canci, Jung Kyu. (2010) Rational periodic points for quadratic maps. Annales de l'Institut Fourier, 60 (3). p. 33.

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Let K be a number field. Let S be a finite set of places of K containing all the archimedean ones. Let R S be the ring of S-integers of K. In the present paper we consider endomorphisms of ℙ 1 of degree 2, defined over K, with good reduction outside S. We prove that there exist only finitely many such endomorphisms, up to conjugation by PGL 2 (R S ), admitting a periodic point in ℙ 1 (K) of order >3. Also, all but finitely many classes with a periodic point in ℙ 1 (K) of order 3 are parametrized by an irreducible curve.
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:Institut Fourier
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:29 Nov 2017 10:02
Deposited On:29 Nov 2017 10:02

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