Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois representations attached to abelian varieties of CM type   Let $K$ be a number field, $A/K$ be an absolutely simple abelian variety of
CM type, and $\ell$ be a prime number. We give explicit bounds on the degree
over $K$ of the division fields $K(A[\ell^n])$, and when $A$ is an elliptic
curve we also describe the full Galois group of $K(A_{\text{tors}})/K$. This
makes explicit previous results of Serre and Ribet, and strengthens a theorem
of Banaszak, Gajda and Kraso\'n. Our bounds are especially sharp in case the CM
type of $A$ is nondegenerate.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas