Families of polynomials of every degree with no rational preperiodic points
نویسندگان
چکیده
منابع مشابه
Preperiodic points for families of rational maps
Let X be a smooth curve defined over Q̄, let a, b ∈ P(Q̄) and let fλ(x) ∈ Q̄(x) be an algebraic family of rational maps indexed by all λ ∈ X(C). We study whether there exist infinitely many λ ∈ X(C) such that both a and b are preperiodic for fλ. In particular, we show that if P,Q ∈ Q̄[x] such that deg(P ) 2 + deg(Q), and if a, b ∈ Q̄ such that a is periodic for P (x)/Q(x), but b is not preperiodic f...
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Given a global field K and a polynomial φ defined over K of degree at least two, Morton and Silverman conjectured in 1994 that the number of K-rational preperiodic points of φ is bounded in terms of only the degree of K and the degree of φ. In 1997, for quadratic polynomials over K = Q, Call and Goldstine proved a bound which was exponential in s, the number of primes of bad reduction of φ. By ...
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ژورنال
عنوان ژورنال: Comptes Rendus. Mathématique
سال: 2021
ISSN: 1778-3569
DOI: 10.5802/crmath.173