Integral Points on Generic Fibers
نویسنده
چکیده
Let P (x, y) be a rational polynomial. If the curve (P (x, y) = k), k ∈ Q, is irreducible and admits an infinite number of points whose coordinates are integers, Siegel’s theorem implies that the curve is rational. We deal with the case where k is a generic value and prove, in the spirit of the Abhyankar-MohSuzuki theorem, that there exists an algebraic automorphism sending P (x, y) to the polynomial x or to x − `y, ` ∈ N. Moreover for such curves we give a sharp bound for the number of integral points (x, y) with x and y bounded.
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