On the Mordell-Weil group of certain abelian varieties defined over the rational function field
نویسندگان
چکیده
منابع مشابه
On the Mordell-weil Rank of an Abelian Variety over a Number Field
Let K be a number field and A an abelian variety over K. The K-rational points of A are known to constitute a finitely generated abelian group (Mordell-Weil theorem). The problem studied in this paper is to find an explicit upper bound for the rank r of its free part in terms of other invariants of A/K. This is achieved by a close inspection of the classical proof of the so-called ‘weak Mordell...
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This is an introductory exposition to background material useful to appreciate various formulations of the Mordell–Lang conjecture (now established by recent spectacular work due to Vojta, Faltings, Hrushovski, Buium, Voloch, and others). It gives an exposition of some of the elementary and standard constructions of algebro-geometric models (rather than model-theoretic ones) with applications (...
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We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y = x + n, n ∈ Z) over Q with three explicit integral points. We show that the points are independent in certain cases. We describe how to compute bounds of the canonical heights of the points. Using the result we show that any pair in the three points can always be a part of a basis of the free part of the Mord...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1991
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(05)80034-4