This is a report on work in progress with Gan and Sawin.

Let $G$ be a reductive group over a local field $F$ of characteristic $p$.

Genestier and V. Lafforgue have constructed a semi-simple local Langlands

parametrization for irreducible admissible representations of $G$, with values in the $\ell$-adic points

of the $L$-group of $G$; the local parametrization is compatible with Lafforgue's global

parametrization of cuspidal automorphic representations. Using this parametrization and the

theory of Frobenius weights, we can define what it means for a representation of $G$ to be {\it pure}.

If $G$ is split semisimple, we have shown that a pure supercuspidal representation that is

compactly induced has {\it ramified} local parameter, provided the field of constants in $F$ has

at least $3$ elements. The result applies to all pure supercuspidals when $p$ is prime to the order of the

Weyl group of $G$. It follows that if the parameter of a pure representation $\pi$ is unramified then $\pi$ is a

constituent of an unramified principal series. We are also able to prove in some cases that the

ramification is wild, and we derive some restrictions on parameters of supercuspidals that

are not pure. The talk will begin with a review of expected properties of the local Langlands

correspondence.