satisfies (iii) and (iv). If $w_{x,v}$ is a product of distinct simple reflections for all places $v$ of $F^+$ dividing $p$, then $x$ is classical.

Note that the assumption on the $w_{x,v}$ in Theorem \[mainintro\] is empty when $n=2$, and already this $n=2$ case was not previously known (to the knowledge of the authors). The noncritical case of Theorem \[mainintro\], i.e. the special case where all the $w_{x,v}$ are trivial, is already known and due to Chenevier ([@Chenevierfern Prop.4.2]). Thus the main novelty, and difficulty, in Theorem \[mainintro\] is that it deals with possibly critical (though not too critical) points.

In fact we give a more general classicality criterion and prove that it is satisfied under the assumptions of Theorem $\ref{mainintro}$. This criterion is formulated in terms of the rigid analytic space of trianguline representations $X_{\rm tri}^\square({\overline{\rho}}_{x,v})$ defined in [@HellmannFS] and [@BHS §2.2]. For every $v\in S_p$ there is a canonical morphism from the eigenvariety to $X_{\rm tri}^\square({\overline{\rho}}_{x,v})$.

\[mainintro2\] Let $p>2$ and assume that the group $G$ and the tame level satisfy (i) and (ii). Let $x$ be an overconvergent form of classical weight such that $\rho_x$ is crystalline and satisfies (iii) and (iv). If for any $v\in S_p$ the 