COUNTING ELLIPTIC SURFACES OVER FINITE FIELDS

被引：0

作者：

de Jong, A. J. ^{[1
]}

机构：

[1] MIT, Cambridge, MA 02139 USA

来源：

MOSCOW MATHEMATICAL JOURNAL | 2002年 / 2卷 / 02期

关键词：

Elliptic curves; elliptic surfaces; rank; average rank; Selmer group;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We count the number of isomorphism classes of elliptic curves of given height d over the field of rational functions in one variable over the finite field of q elements. We also estimate the number of isomorphism classes of elliptic surfaces over the projective line, which have a polarization of relative degree 3. This leads to an upper bound for the average 3-Selmer rank of the aforementionned curves. Finally, we deduce a new upper bound for the average rank of elliptic curves in the large d limit, namely the average rank is asymptotically bounded by 1.5 + O(1/q).

引用

页码：281 / 311

页数：31

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