13 problems

Let $x=(\rho,\underline{\delta})\in Y(U^p,\overline{\rho})$ be a crystalline generic strictly dominant point. For each $v\mid p$, let…

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

Regular crystalline-point closure conjecture. The Zariski closure of the set of regular crystalline points in $\mathcal{X}_{\overline\rho}$ is a union of irreducible components.

Let $X_{\mathfrak p}(\overline\rho)$ be the relevant trianguline eigenvariety, let $y=(r_y,\delta)$ be the point under consideration, and let $\chi_J^c$ be the characters defined f…

Let $\widehat{T}_L^{\mathrm{spl}}$ be the subspace of characters whose adjacent ratios are special, let $K_0({\lambda}_{\mathbf h},\underline{\delta}_{\mathrm{sm}})$ be the free ab…

Let $L$ be a finite extension of $\mathbb{Q}_p$, let $k_L$ be its residue field, and let $\rho:G_{\mathbb{Q}_p}\rightarrow GL_n(L)$ be a trianguline representation with parameters…

Breuil–Hellmann–Schraen's conjecture. For any irreducible component $\Xfrak^p$ of $\Xfraknotp$, the rigid analytic subvariety $\Xaut\subseteq\Xtrip$ is equal to $\Xtriptilde$. In p…

For each place $v\mid p$, let $X_{\mathrm{tri}}^\square(\overline\rho_{\widetilde{v}})$ be the trianguline deformation space, and let…

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…

Let $r\in\mathfrak{X}_{\overline r}(L)$ be a generic trianguline representation, and let $\Pi$ be an absolutely irreducible constituent of a locally $\mathbb{Q}_p$-analytic princip…

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…