Asymptotic Variation of Elementary Abelian p-Extensions over P¹

In this paper, we prove that there exists a Zariski dense open subset U in the parameter space of all elementary p-covers of the projective line that ramified at exactly one point, defined over the rationals, such that for every curve X in U (Q) and for any prime p large enough, the reduction of X at all primes lying over p achieves its generic Newton slopes.