Preperiodic points for rational functions defined over a global field in terms of good reduction
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- by Jung Kyu Canci and Laura Paladino PDF
- Proc. Amer. Math. Soc. 144 (2016), 5141-5158 Request permission
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.References
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Additional Information
- Jung Kyu Canci
- Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
- MR Author ID: 803697
- Email: jungkyu.canci@unibas.ch
- Laura Paladino
- Affiliation: Dipartimento di Matematica, Università 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
- MR Author ID: 884025
- Email: paladino@mail.dm.unipi.it, paladino@mat.unical.it
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5141-5158
- MSC (2010): Primary 37P05, 37P35; Secondary 11D45
- DOI: https://doi.org/10.1090/proc/13096
- MathSciNet review: 3556260