Height uniformity for integral points on elliptic curves
نویسندگان
چکیده
منابع مشابه
Uniformity of Stably Integral Points on Elliptic Curves
Let X be a variety of logarithmic general type, defined over a number field K. Let S be a finite set of places in K and let OK,S be the ring of S-integers. Suppose that X is a model of X over Spec OK,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 (OK,S) is not Zariski de...
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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...
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By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demjanenko [L3] states that, for a quasiminimal model of E over K, this number is bounded by a constant depending only on the rank of E over K and on K (see also [HSi], [Zi4]). This conjecture was proved by Silverman [Si1] for elliptic curv...
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If E is a minimal elliptic curve defined over Z, we obtain a bound C, depending only on the global Tamagawa number of E, such that for any point P ∈ E(Q), nP is integral for at most one value of n > C. As a corollary, we show that if E/Q is a fixed elliptic curve, then for all twists E′ of E of sufficient height, and all torsion-free, rank-one subgroups Γ ⊆ E′(Q), Γ contains at most 6 integral ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03760-8