The number of monodromy representations of Abelian varieties of low p-rank

In the last section we prove a divisibility theorem about the number of homomorphisms from certain semidirect products of profinite groups into finite groups. As a corollary, we deduce that when λ=0,#Hom(π1ét(Ag,a),GLn(Fq))|GLn(Fq)| is a Laurent polynomial in q.