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In this paper we study skeleta of residually tame coverings of a marked curveover a non-archimedean field. We first generalize a result by Liu and Lorenziniby proving a simultaneous semistable reduction theorem for residually tamecoverings. We then use this to construct a functor from the category ofresidually tame coverings of a marked curve $(X,D)$ to the category of tamecoverings of a metrized complex $\Sigma$ associated to $(X,D)$. We enhance thelatter category by adding a set of gluing data to every covering and we showthat this yields an equivalence of categories. Using this equivalence, we thendefine filtrations of the fundamental group of the marked curve, giving forinstance the absolute decomposition and inertia groups of the metrized complex.We then use the analytic slope formula to prove that the extensions that arisefrom the abelianizations of the decomposition and inertia quotients coincidewith the extensions that arise from the toric and connected parts of theanalytic Jacobian of the curve.

Skeletal filtrations of the fundamental group of a non-archimedean curve