Deformation functors of local actions

We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a deformation functor of a local $G$-action as a smooth extension of a fibered product of functors related to a subgroup and a quotient group of $G$.

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