Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the modularity of supersingular elliptic curves over certain totally
  real number fields   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 $\mathbb{Q}(\sqrt{2})$.

13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio