The distribution of class groups of function fields

Abstract

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