The ABC Conjecture Implies Vojta's Height Inequality for Curves
نویسندگان
چکیده
منابع مشابه
The Abc Conjecture Implies Roth’s Theorem and Mordell’s Conjecture
We present in a unified way proofs of Roth’s theorem and an effective version of Mordell’s conjecture, using the ABC conjecture. We also show how certain stronger forms of the ABC conjecture give information about the type of approximation to an algebraic number.
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The ABC–conjecture was first formulated by David Masser and Joseph Osterlé (see [Ost]) in 1985. Curiously, although this conjecture could have been formulated in the last century, its discovery was based on modern research in the theory of function fields and elliptic curves, which suggests that it is a statement about ramification in arithmetic algebraic geometry. The ABC–conjecture seems conn...
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Vojta’s Conjectures are well known to imply a wide range of results, known and unknown, in arithmetic geometry. In this paper, we add to the list by proving that they imply that rational points tend to repel each other on algebraic varieties with nonnegative Kodaira dimension. We use this to deduce, from Vojta’s Conjectures, conjectures of Batyrev-Manin and Manin on the distribution of rational...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2002
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(01)92769-6