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

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

2007-08-29

arxiv.org/abs/0708.3942v1

Mathematics

Number Theory

36 pages (revised version of 2002 preprint)

Scientific paper

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 $\mathbb{Q}(\sqrt{2})$.

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