Congruent numbers, elliptic curves, and the passage from the local to the global

被引：0

作者：

Dalawat C.S. ^{[1
]}

机构：

[1] Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, Chhatnag Road

来源：

Resonance | 2009年 / 14卷 / 12期

关键词：

Birch and Swinnerton-Dyer conjecture; Congruent numbers; Elliptic curves; Hasse principle; Shafarevich-Tate conjecture;

D O I：

10.1007/s12045-009-0113-6

中图分类号：

学科分类号：

摘要：

The ancient unsolved problem of congruent numbers has been reduced to one of the major questions of contemporary arithmetic: the finiteness of the number of curves over Q which become isomorphic at every place to a given curve. We give an elementary introduction to congruent numbers and their conjectural characterisation, discuss local-to-global issues leading to the finiteness problem, and list a few results and conjectures in the arithmetic theory of elliptic curves. © 2009 Indian Academy of Sciences.

引用

页码：1183 / 1205

页数：22

共 18 条

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