Uniformity of rational points

Uniformity of Rational Points

1. Uniformity and correlation 1 1.

Distribution of Rational Points: A Survey

Rational Points

is known to have only finitely many triples of positive integer solutions x, y, z for a given n > 2 (Faltings, 1983). In Chapter 11, special situations are described in which more precise information is accessible. For example, if x is in S, then n is bounded by a computable number C5 = Cb(pv ..., p8). From these examples, it should be clear that the book is a mine of information for workers in...

Uniformity of stably integral points on elliptic

0. Introduction Let X be a variety of logarithmic general type, deened over a number eld K. Let S be a nite set of places in K and let O K;S be the ring of S-integers. Suppose that X is a model of X over Spec O K;S. As a natural generalizasion of theorems of Siegel and Faltings, It was conjectured by S. Lang and P. Vojta ((Vojta], conjecture 4.4) that the set of S-integral points X(O K;S) is no...

K3 Surfaces, Rational Curves, and Rational Points

We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...