On the modularity of supersingular elliptic curves over certain totally real number fields

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We study generalisations to totally real fields of methods originating with Wiles and Taylor-Wiles. In view of the results of Skinner-Wiles on elliptic curves with ordinary reduction, we focus here on the case of supersingular reduction. Combining these, we then obtain some partial results on the modularity problem for semistable elliptic curves, and end by giving some applications of our results, for example proving the modularity of all semistable elliptic curves over $\mathbb{Q}(\sqrt{2})$.
36 pages (revised version of 2002 preprint)

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Number Theory, 11F41 (Primary), 11F80, 11G05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/136924

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.3942
 http://arxiv.org/abs/0708.3942

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arXiv