A GIT construction of moduli spaces of stable maps in positive characteristic

In a previous paper, the author and Swinarski constructed the moduli spaces of stable maps, ℳ̄g, n(Pr, d) via geometric invariant theory (GIT). That paper required the base field to be the complex numbers, a restriction that this paper removes: here the coarse moduli spaces of stable maps are constructed via GIT over a more general base.