The formal Teichmüller space for stable Mumford curves (Q1325298)

The author studies stable curves over a complete local ring \({\mathfrak o}\) which have a totally degenerated special fibre. The curves are obtained by an action of a free group \(F_ g\) on a tree of projective lines (\(F_ g\)-trees). -- The formal Teichmüller space is a formal neighbourhood of the subspace corresponding to totally degenerated curves in the moduli space of \(F_ g\)-trees. This moduli space is not a scheme but only a pro-scheme. In this paper the formal Teichmüller space is constructed by glueing completions of affine schemes which cover the moduli space of \(F_ g\)- trees. The completions are taken along the subspaces corresponding to totally degenerated curves.