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

JOURNAL OF NUMBER THEORY

卷:137

Article

Pal, Ambrus

关键词: Elliptic surfaces;    Mordell-Weil ranks;    Hodge theory;   

DOI  :  10.1016/j.jnt.2013.11.009

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free