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引用次数: 0
摘要
在本文中，我们将 Dimitrov 等人[Uniformity in Mordell-Lang for curves, Ann. of Math. (2) 194(1) (2021) 237-298] 的统一性结果扩展到维数二，并利用它得到了非全椭圆非双曲曲线所有二次点集合的心数的统一约束，该约束只取决于莫德尔-韦尔等级、曲线的属和数域的度。
In this paper, we extend a uniformity result of Dimitrov et al. [Uniformity in Mordell-Lang for curves, Ann. of Math. (2) 194(1) (2021) 237–298] to dimension two and use it to get a uniform bound on the cardinality of the set of all quadratic points for non-hyperelliptic non-bielliptic curves which only depend on the Mordell–Weil rank, the genus of the curve and the degree of the number field.
期刊介绍：
This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.
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