Asymptotic low slopes of toric exponential sums

Source abstract

Let $Δ$ be an integral Newton polytope containing the origin. We prove that the generic Newton slopes corresponding to Hodge slopes strictly smaller than one differ from their Hodge values by $O_Δ(p^{-1})$. No hypothesis is imposed on the semigroup generated by the lattice points of $Δ$. The proof combines an auxiliary prime and the Cartier operator to show that a coefficient of each required Dwork principal minor is nonzero. When the origin is interior to $Δ$, duality gives the same estimate for the corresponding high slopes and, in dimension two, for all slopes.