Author's Final Manuscript
Journal für die reine und angewandte Mathematik
We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in terms of “critical types” and when our bound is minimized it matches the dimension of the eigenvariety. In those cases, which we explicitly determine, the eigenvariety is necessarily smooth and our proof also shows that the completed local ring on the eigenvariety is naturally a certain universal Galois deformation ring.
Bergdall, John. "Smoothness of de nite unitary eigenvarieties at critical points." Journal für die reine und angewandte Mathematik, forthcoming (published online 2018).