Number Theory Seminar

Given a family of abelian covers of P¹ and a prime p of good reduction, by considering the associated Deligne–Mostow Shimura variety, we obtain new lower bounds for the Ekedahl-Oort type, and the Newton polygon, at p of the curves in the family. In this paper, we investigate whether such lower bounds are sharp. In particular, we prove sharpeness when the number of branching points is at most five and p sufficiently large. Our result is a generalization of the result by Bouw, which proves the analogous statement for the p-rank, and it relies on the notion of Hasse-Witt triple introduced by Moonen.