Arithmetic of Free Group Character Varieties

Let Hom(F_r ,G) denote the collection of
representations of a free group of rank r into
a group G. In previous work, we showed how to count the total
number of representations when G is SL(n,Ζp). We will focus our
attention on Hom(F_r ,SL(2,Ζ_p)) and count the number of conjugation orbits; that is, the cardinality
of Hom(F_r ,SL(2,Ζ_p))  / SL(2,Ζ_p).