  In this note we show that any basic abelian variety with additional
structures over an arbitrary algebraically closed field of characteristic $p>0$
is isogenous to another one defined over a finite field. We also show that the
category of abelian varieties over finite fields up to isogeny can be embedded
into the category of basic abelian varieties with suitable endomorphism
structures. Using this connection, we derive a new mass formula for a finite
orbit of polarized abelian surfaces over a finite field.
