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

Adel Betina, Shaunak V. Deo, Francesc Fité

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 $p$-ad…