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

@article{Betina2018OnTH,
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},
year={2018}
}
• Published 29 June 2018
• Mathematics
• 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
1 Citations
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