### 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
*S*(**F**_{q}*,n*)
approaches 1 as *q* approaches infinity over the prime powers.

Everett W. Howe and Hui June Zhu <however@alumni.caltech.edu, zhu@alum.calberkeley.org>