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arXiv · 0704.3783

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

Chandan Singh Dalawat
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Abstract

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 $\bf Q$ 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.

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Chandan Singh Dalawat. 2007-04-28. Congruent numbers, elliptic curves, and the passage from the local to the global. https://arxiv.org/abs/0704.3783

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