let $x$ be a smooth, affine, geometrically connected curve over a finite field of characteristic $p > 2$. let $\rho:\pi_1(x) \to \mathbb{c}^\times$ be a character of finite order $p^n$. if $\rho\neq 1$, then the artin $l$-function $l(\rho,s)$ is a polynomial, and a theorem of kramer-miller states that its $p$-adic newton polygon $\mathrm{np}(\rho)$ is bounded below by a certain hodge polygon $\mathrm{hp}(\rho)$ which is defined in terms of local monodromy invariants. in this talk we discuss the interaction between the polygons $\mathrm{np}(\rho)$ and $\mathrm{hp}(\rho)$. our main result states that if $x$ is ordinary, then $\mathrm{np}(\rho)$ and $\mathrm{hp}(\rho)$ share a vertex if and only if there is a corresponding vertex shared by certain ``local" newton and hodge polygons associated to each ramified point of $\rho$. as an application, we give a local criterion that is necessary and sufficient for $\mathrm{np}(\rho)$ and $\mathrm{hp}(\rho)$ to coincide. this is joint work with joe kramer-miller.