12 problems

Let the decompositions proved in the theorem, together with the known decompositions for parabolic (parahoric) subgroups in Tits theory, be formulated using the rings…

Let $X$ be the building of $G$, and let ${\mathscr{S}}$ be the Schneider–Stuhler $G$-equivariant sheaf associated with an irreducible supercuspidal representation. A basic elementa…

Let $\Delta$ be the Bruhat–Tits building, let $\mathbb{X}$ be the coefficient system, let $X_{0,2}$ be the specified set of edges, and let $I$ be the relevant subgroup. Let…

Local exactness conjecture. When (A) holds, namely when $\mathcal{X}$ is a complete region of $\Delta$, the local oriented chain complex is exact.

Let $\Delta$ be the Bruhat–Tits building of dimension $d$, let $\mathbb{X}$ be the coefficient system, and let $\mathcal{X}$ be a set of facets. For each $i\leq d$, write…

Let $K$ be a discretely valued field and let ${\mathcal E}$ be a toric vector bundle over the toric variety $X$ of rank $r$. Let $\Phi_{{\mathcal E}}$ denote the piecewise linear m…

Let $G$ be a reductive algebraic group over $\operatorname{Spec}(\mathcal{O})$, and let $\mathfrak{X}_\Sigma$ be a toric scheme associated with a fan $\Sigma$. A toric principal…

Let $G$ be a reductive group with a fixed cuspidal datum and an irreducible supercuspidal representation $\pi$ such that $(J,\lambda)$ is a $[G,\pi]_G$-type. For a point $y$ in the…

Let $\mathcal{B}$ be the Bruhat–Tits building associated with $\mathrm{PGL}_{d}(F)$, where $F$ is a local field and $d\geq3$. For a finite quotient $X$ of $\mathcal{B}$, let…

Let a Moufang polygon of exceptional type be defined over a field with a complete valuation, and suppose that, where applicable, the valuation is preserved by an involution or Tits…

Let $G$ be a connected reductive algebraic group defined over a field $K$ with a valuation $\nu$. The associated Bruhat–Tits building, when it exists, is denoted by $I_{K,\nu}(G)$.…

Let $Y(z)=(Y_1(z),\ldots,Y_n(z))$ be an $n$-tuple of invertible $d\times d$-matrices over $\mathbb{Q}(z)$, and let $\mathcal{B}$ be the Bruhat–Tits building. The matrices are not a…