The distribution of class groups of function fields

For any sufficiently general family of curves over a finite field FqFq and any elementary abelian ℓℓ-group H   with ℓℓ relatively prime to q, we give an explicit formula for the proportion of curves C   for which Jac(C)[ℓ](Fq)≅HJac(C)[ℓ](Fq)≅H. In doing so, we prove a conjecture of Friedman and Washington.