On the Hilbert eigenvariety at exotic and CM classical weight 1 points

  title={On the Hilbert eigenvariety at exotic and CM classical weight 1 points},
  author={Adel Betina and Shaunak V. Deo and Francesc Fit'e},
  journal={arXiv: Number Theory},
Let $F$ be a totally real number field and let $f$ be a classical cuspidal $p$-regular Hilbert modular eigenform over $F$ of parallel weight $1$. Let $x$ be the point on the $p$-adic Hilbert eigenvariety $\mathcal E$ corresponding to an ordinary $p$-stabilization of $f$. We show that if the $p$-adic Schanuel Conjecture is true, then $\mathcal E$ is smooth at $x$ if $f$ has CM. If we additionally assume that $F/\mathbb Q$ is Galois, we show that the weight map is \'etale at $x$ if $f$ has either… Expand
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