Minimal ramification and the inverse Galois problem over the rational   function field $\mathbb{F}_p(t)$
  The inverse Galois problem is concerned with finding a Galois extension of a field $K$ with given Galois group. In this paper we consider the particular case where the base field is $K=\F_p(t)$. We give a conjectural formula for the minimal number of primes, both finite and infinite, ramified in $G$-extensions of $K$, and give theoretical and computational proofs for many cases of this conjecture. 
Meghan De Witt
math.NT