Which weakly ramified group actions admit a universal formal deformation?

Details Which weakly ramified group actions admit a universal formal deformation? Which weakly ramified group actions admit a universal formal deformation?

2007-08-24

arxiv.org/abs/0708.3279v3

Mathematics

Algebraic Geometry

16 pages; further minor corrections

Scientific paper

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.

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