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The coefficient space is a kind of resolution of singularities of the universal flat deformation space for a given Galois representation of some local field. It parameterizes (in some sense) the finite flat models for the Galois representation. The aim of this note is to determine the image of the coefficient space in the universal deformation space.
Let $mathcal{M}(n,m;F bp^n)$ be the configuration space of $m$-tuples of pairwise distinct points in $F bp^n$, that is, the quotient of the set of $m$-tuples of pairwise distinct points in $F bp^n$ with respect to the diagonal action of ${rm PU}(1,n;
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Grassmannian. It has all the properties asked for by Teixidor.
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