  The endomorphism ring End(A) of an abelian variety A is an order in a
semi-simple algebra over Q. The co-index of End(A) is the index to a maximal
order containing it. We show that for abelian varieties of fixed dimension over
any algebraically closed field of characteristic p>0, the p-exponents of the
co-indices of their endomorphism rings are bounded. We also give a few
applications to this finiteness result.
