Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on Automorphy of Residually Dihedral Representations   We prove automorphy lifting results for geometric representations $\rho:G_F
\rightarrow GL_2(\mathcal{O})$, with $F$ a totally real field, and
$\mathcal{O}$ the ring of integers of a finite extension of $\mathbb{Q}_p$ with
$p$ an odd prime, such that the residual representation $\bar{\rho}$ is totally
odd and induced from a character of the absolute Galois group of the quadratic
subfield $K$ of $F(\zeta_p)/F$. Such representations fail the Taylor-Wiles
hypothesis and the patching techniques to prove automorphy do not work. We
apply this to automorphy of elliptic curves $E$ over $F$, when $E$ has no $F$
rational 7-isogeny and such that the image of $G_F$ acting on $E[7]$ normalizes
a split Cartan subgroup of $GL_2(\mathbb{F}_7)$.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph