  Consider a formal (mixed-characteristic) deformation functor D of a
representation of a finite group G as automorphisms of a power series ring
k[[t]] over a perfect field k of positive characteristic. Assume that the
action of G is weakly ramified, i.e., the second ramification group is trivial.
Examples of such representations are provided by a group action on an ordinary
curve: the action of a ramification group on the completed local ring of any
point on such a curve is weakly ramified.
  We prove that the only such D that are not pro-representable occur if k has
characteristic two and G is of order two or isomorphic to a Klein group.
Furthermore, we show that only the first of those has a non-pro-representable
equicharacteristic deformation functor.

Algebraic Geometry;Number Theory