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Preperiodic points for rational functions defined over a global field in terms of good reduction


Authors: Jung Kyu Canci and Laura Paladino
Journal: Proc. Amer. Math. Soc. 144 (2016), 5141-5158
MSC (2010): Primary 37P05, 37P35; Secondary 11D45
DOI: https://doi.org/10.1090/proc/13096
Published electronically: April 20, 2016
MathSciNet review: 3556260
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Abstract: Let $ \phi $ be an endomorphism of the projective line defined over a global field $ K$. We prove a bound for the cardinality of the set of $ K$-rational preperiodic points for $ \phi $ in terms of the number of places of bad reduction. The result is completely new in the function field case and is an improvement of the number field case.


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Additional Information

Jung Kyu Canci
Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
Email: jungkyu.canci@unibas.ch

Laura Paladino
Affiliation: Dipartimento di Matematica, Universit\aca di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy – and – Dipartimento di Matematica e Informatica, Università della Calabria, Ponte Pietro Bucci Cubo 30B, 87036 Arcavacata di Rende (CS), Italy
Email: paladino@mail.dm.unipi.it, paladino@mat.unical.it

DOI: https://doi.org/10.1090/proc/13096
Received by editor(s): March 21, 2015
Received by editor(s) in revised form: September 4, 2015, and January 8, 2016
Published electronically: April 20, 2016
Additional Notes: The second author was partially supported by Istituto Nazionale di Alta Matematica, grant research Assegno di ricerca Ing. G. Schirillo, and partially supported by the European Commission and by Calabria Region through the European Social Fund.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2016 American Mathematical Society