  We 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.
