8 problems

Incidence-algebra discrepancy conjecture. There exists a group $G$ for which the global dimension of the rational incidence algebra for ${\operatorname{Sub}_G}/G$ differs from the…

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…

Schneider–Ollivier's surjectivity conjecture. The canonical morphism $\mathbb{X}^*\to\mathcal{H}$ is a surjection.

Let $k$ be a field of characteristic $0$ equipped with a complex embedding, and let $\operatorname{DA}^{\mathrm{\acute{e}t}}(-,\mathbb{Q})$ and…

Let $\Omega_q$ be the collection of simplices under consideration, and let $K_{\Sigma}^{\lambda_{\rm max}}$ denote the $\lambda_{\rm max}$-isotypic component associated with…

Let $F$ be a non-archimedean local field, let $G={\rm GL}(N,F)$ with $N\geq 2$, and let $\pi$ be a smooth complex representation of $G$ lying in the Bernstein block $\cal B(\pi)$ o…