Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non-existence of exceptional automorphisms on Shimura curves   We study the group of automorphisms of Shimura curves $X_0(D, N)$ attached to
an Eichler order of square-free level $N$ in an indefinite rational quaternion
algebra of discriminant $D>1$. We prove that, when the genus $g$ of the curve
is greater than or equal to 2, $\Aut (X_0(D, N))$ is a 2-elementary abelian
group which contains the group of Atkin-Lehner involutions $W_0(D, N)$ as a
subgroup of index 1 or 2. It is conjectured that $\Aut (X_0(D, N)) = W_0(D, N)$
except for finitely many values of $(D, N)$ and we provide criteria that allow
us to show that this is indeed often the case. Our methods are based on the
theory of complex multiplication of Shimura curves and the Cerednik-Drinfeld
theory on their rigid analytic uniformization at primes $p\mid D$.

22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int