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On the eigenvariety of Hilbert modular forms at classical parallel weight one points with dihedral projective image
We show that the $p$-adic eigenvariety constructed by Andreatta-Iovita-Pilloni, parameterizing cuspidal Hilbert modular eigenforms defined over a totally real field $F$, is smooth at certain classical parallel weight one points which are regular at every place of $F$ above $p$ and also determine whether the map to the weight space …