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Topology and geometry of the Berkovich ramification locus for rational functions, I

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We initiate a detailed study of the ramification locus for projective endomorphisms of the Berkovich projective line—the non-Archimedean analog of the Riemann sphere.

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References

  1. Baker, M., Conrad, B., Dasgupta, S., Kedlaya, K. S., Teitelbaum J.: p-adic geometry. In: Savitt, D., Dinesh S. (ed.) Thakur University Lecture Series, vol. 45. American Mathematical Society, Providence (2008). Lectures from the 10th Arizona Winter School held at the University of Arizona, Tucson, AZ, March 10–14, 2007

  2. Baker, M., Rumely R.: Potential theory and dynamics on the Berkovich projective line. In: Mathematical Surveys and Monographs, vol. 159. American Mathematical Society, Providence (2010)

  3. Berkovich, V.G.: Spectral theory and analytic geometry over non-Archimedean fields. Mathematical Surveys and Monographs, vol. 33. American Mathematical Society, Providence (1990)

  4. Berkovich, V.G.: Étale cohomology for non-Archimedean analytic spaces. Inst. Hautes Études Sci. Publ. Math., (78), 5–161 (1993)

  5. Faber, X.: Rational functions with a unique critical point. (Preprint, to appear in Int. Math. Res. Not. doi:10.1093/imrn/rns239). arXiv:1102.1433v2 [math.NT] (2012)

  6. Faber, X.: Topology and geometry of the Berkovich ramification locus for rational functions, II (Preprint, arXiv:1104.0943v3 [math.NT], to appear in Math. Ann.) doi:10.1007/s00208-012-0872-3(2012)

  7. Favre C., Rivera-Letelier J.: Théorie ergodique des fractions rationnelles sur un corps ultramétrique. Proc. Lond. Math. Soc. (3) 100(1), 116–154 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kiwi J.: Puiseux series polynomial dynamics and iteration of complex cubic polynomials. Ann. Inst. Fourier (Grenoble) 56(5), 1337–1404 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kiwi J.: Rescaling limits of complex rational maps (2012, preprint). arXiv:1211.3397 [math.DS]

  10. Poineau, J.: Les espaces de Berkovich sont angéliques. Bull. Soc. Math. Fr. 141(2) (2013). arXiv:arXiv:1105.0250v5 [math.AG]

  11. Rivera-Letelier, J.: Dynamique des fonctions rationnelles sur des corps locaux. Geometric methods in dynamics. II. Astérisque xv(287), 147–230 (2003)

  12. Rivera-Letelier J.: Espace hyperbolique p-adique et dynamique des fonctions rationnelles. Compositio Math. 138(2), 199–231 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rivera-Letelier J.: Points périodiques des fonctions rationnelles dans l’espace hyperbolique p-adique. Comment. Math. Helv. 80(3), 593–629 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Robert, A. M.: A course in p-adic analysis. Graduate Texts in Mathematics, vol. 198. Springer, New York (2000)

  15. Trucco, E.: Wandering Fatou components and algebraic Julia sets. Bull. Soc. Math. Fr. (2012, To appear)

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Correspondence to Xander Faber.

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Faber, X. Topology and geometry of the Berkovich ramification locus for rational functions, I. manuscripta math. 142, 439–474 (2013). https://doi.org/10.1007/s00229-013-0611-4

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  • DOI: https://doi.org/10.1007/s00229-013-0611-4

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