6 problems

The local companion points conjecture. The following conditions are equivalent:

Reductive-group triangulation uniqueness conjecture. Then $D$ has at most one triangulation of parameter $\delta$.

Let $\mathcal{R}$ be a refinement, let $\lambda$ be the algebraic weight appearing in the associated locally analytic representation, and let $w_0$ be the longest Weyl-group elemen…

BHS automorphic trianguline subvariety conjecture. The rigid subvariety $X_{\rm tri}^{\mathfrak{X}^p\rm-aut}(\overline{\rho}_p)$ does not depend on $\mathfrak{X}^p$ and is isomorph…

Let $x\in X_{\rm tri}^\square(\overline{r})$ be a crystalline strictly dominant point whose Frobenius eigenvalues $(\varphi_1,\dots,\varphi_n)$ are pairwise distinct. Let $w_x$ be…

Let $\mathfrak{X}^p$ be an irreducible component of $\mathfrak{X}^\square_{\bar{\rho}^p}$. Let $X$ be an irreducible component of $X_{\rm tri}^\square(\bar{\rho}_p)$. By definition…