belyi's theorem says that on one hand, a curve over a field of characteristic 0 that admits a finite map to $\mathbf{p}^1$ ramified over at most three points must descend to a subfield algebraic over $\mathbb{q}$, and on the other hand any curve over such a subfield does indeed admit such a morphism (without any further base extension). one might ask whether a similar statement holds over a field of characteristic $p$, replacing $\mathbb{q}$ with $\mathbb{f}_p$. for general morphisms this is false, but it becomes true if we restrict to tamely ramified morphisms to $\mathbf{p}^1$. such a statement was originally given by saidi, in which the ``other hand'' assertion was made conditional on the existence of some tamely ramified morphism from the given curve to $\mathbf{p}^1$. in the pre-talk, we will discuss how to establish existence of a tamely ramified morphism in characteristic \mbox{$p\>2$}. this is ``classical'' over an infinite algebraic extension of $\mathbb{f}_p$; to do it over a fixed finite field requires a density statement in the style of poonen's finite field bertini theorem. in the talk proper, we will discuss work of sugiyama-yasuda that establishes the existence of a tamely ramified morphism when the base field is algebraically closed of characteristic 2. the case where the base field is finite of characteristic 2 requires a further geometric reinterpretation of the key construction of sugiyama-yasuda; this is joint work with daniel litt and jakub witaszek.