5 problems

Let ${\bf G}$ be the group under consideration, let $\Bbbk$ be the coefficient field, let ${\bf T}$ be its torus, and let $\operatorname{St}$ denote the Steinberg module. For a cha…

Let $v_1,\dots,v_d$ be vectors in general position, let $w_1,\dots,w_d$ be vectors with dual basis of linear functionals $w^1,\dots,w^d$, and let $x\in\mathrm{T}_d$. For positive i…

Let $\Gamma$ be a congruence subgroup of $\operatorname{SL}_3(\mathbb{Z})$, let $E$ be a real quadratic field, and let $H(\Gamma,E)$ be the Hecke-stable subspace of…

Let $A$ be a connected semi-local ring, let $M$ be a finitely generated projective $A$-module of rank $d$, and let $\iota\colon M\to A^d$ be an isomorphism. Define … The elements…

Steinberg-module stability conjecture. For each $i,j\geq 0$, the $\mathrm{VB}_{\mathbb{Z}}/\Gamma(p)$-module