On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field, by Everett W. Howe and Hui June Zhu
We prove that for every field k and every positive
integer n, there exists an absolutely simple
n-dimensional abelian variety over k.
We also prove an asymptotic result for finite fields:
For every finite field k and positive integer n,
we let S(k,n) denote the fraction of the isogeny
classes of n-dimensional abelian varieties over k
that consist of absolutely simple ordinary abelian varieties.
Then for every n the quantity
approaches 1 as q approaches infinity over the prime powers.
Everett W. Howe and Hui June Zhu <firstname.lastname@example.org, email@example.com>