2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61165We compute the dimension of the tangent space to, and the Krull dimension of the pro-representable hull of two deformation functors. The first one is the ``algebraic'' deformation functor of an ordinary curve X over a field of positive charateristic with prescribed action of a finite group G, and the data are computed in terms of the ramification behaviour of X -> G\X. The second one is the ``analytic'' deformation functor of a fixed embedding of a finitely generated discrete group N in PGL(2,K) over a non-archimedean valued field K, and the data are computed in terms of the Bass-Serre representation of N via a graph of groups. Finally, if F is a free subgroup of N such that N is contained in the normalizer of F in PGL(2,K), then the Mumford curve associated to F becomes equipped with an action of N/F, and we show that the algebraic functor deforming the latter action coincides with the analytic functor deforming the embedding of N.31 pages, version 2 contains major changes in section 4 on versal deformationsAlgebraic Geometry14G22, 14D15, 14H37text