Hodge theory and the Mordell-Weil rank of elliptic curves over extensions of function fields

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• 作者：Ambrus P谩l
• 关键词：14J27 ; 11G40
• 刊名：Journal of Number Theory
• 出版年：April, 2014
• 年：2014
• 卷：137
• 期：Complete
• 页码：166-178
• 全文大小：255 K

文摘

We use Hodge theory to prove a new upper bound on the ranks of Mordell-Weil groups for elliptic curves over function fields after regular geometrically Galois extensions of the base field, improving on previous results of Silverman and Ellenberg, when the base field has characteristic zero and the supports of the conductor of the elliptic curve and of the ramification divisor of the extension are disjoint.