Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Split reductions of simple abelian varieties   Consider an absolutely simple abelian variety X over a number field K. If the
absolute endomorphism ring of X is commutative and satisfies certain parity
conditions, then the reduction X_p is absolutely simple for almost all p.
Conversely, if the absolute endomorphism ring of X is noncommutative, then X_p
is reducible for p in a set of positive density.

10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th