Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The splitting of reductions of an abelian variety   Consider an absolutely simple abelian variety A defined over a number field
K. For most places v of K, we study how the reduction A_v of A modulo v splits
up to isogeny. Assuming the Mumford-Tate conjecture for A and possibly
increasing K, we will show that A_v is isogenous to the m-th power of an
absolutely simple abelian variety for all places v of K away from a set of
density 0, where m is an integer depending only on the endomorphism ring
End(A_Kbar). This proves many cases, and supplies justification, for a
conjecture of Murty and Patankar. Under the same assumptions, we will also
describe the Galois extension of Q generated by the Weil numbers of A_v for
most v.

13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess