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Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let α0 ∈ A1(K) ⊂ P1(K) and let Γ0 be the set of the images of α0 under especially all Chebyshev morphisms. Then for any α ∈ A1(K), we show that there are only a finite number of elements in Γ0 which are S-integral on P1 relative to (α). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on P1, which generalizes the above finiteness result for Chebyshev morphisms.
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참고문헌 (7)
참고문헌 신청
D. Grant / 2013 / Integral division points on curves / Compos. Math 149 (12) : 2011 ~ 2035
J. H. Silverman / 1993 / Integer points, Diophantine approximation, and iteration of rational maps / Duke Math. J 71 (3) : 793 ~ 829
J. H. Silverman / 2007 / The Arithmetic of Dynamical Systems, Graduate Texts in Mathematics, 241 / Springer
J. Milnor / 1999 / Dynamics in one complex variable / Friedr. Vieweg & Sohn
P. Habegger / / Distribution of integral division points on the algebraic torus
J. H. Silverman / 1993 / Integer points, Diophantine approximation, and iteration of rational maps / Duke Math. J 71 (3) : 793 ~ 829
J. H. Silverman / 2007 / The Arithmetic of Dynamical Systems, Graduate Texts in Mathematics, 241 / Springer
J. Milnor / 1999 / Dynamics in one complex variable / Friedr. Vieweg & Sohn
P. Habegger / / Distribution of integral division points on the algebraic torus
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