期刊
COMPOSITIO MATHEMATICA
卷 140, 期 3, 页码 567-580出版社
KLUWER ACADEMIC PUBL
DOI: 10.1112/S0010437X03000381
关键词
elliptic n-fold; Mordell-Weil group; Shioda-Tate formula; Nagao formula; Frobenius trace values
类别
In a recent paper, Rosen and Silverman showed that Tate's conjecture on algebraic cycles implies a formula of Nagao, which gives the rank of an elliptic surface in terms of a weighted average of fibral Frobenius trace values. In this article, we extend their result to the case of elliptic threefolds. The main ingredients of our argument are a Shioda-Tate-like formula for elliptic threefolds, and a relation between the 'average' number of rational points on singular fibers and the Galois action on those fibers.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据