2 9 A ug 2 00 7 On the modularity of supersingular elliptic curves over certain totally real number fields
نویسنده
چکیده
We study generalisations to totally real fields of the methods originating with Wiles and Taylor-Wiles ([32], [31]). In view of the results of Skinner-Wiles [26] 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 Q(√ 2).
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