Brück–Santos Rego–Sroka vanishing conjecture for Euclidean Chevalley groups

Let ${\mathfrak{O}}$ be a Euclidean number ring and let ${\mathcal{G}}$ be a Chevalley–Demazure group scheme. Brück–Santos Rego–Sroka's conjecture.

$$H^{\operatorname{vcd}({\mathcal{G}}({\mathfrak{O}}))-i}({\mathcal{G}}({\mathfrak{O}});\mathbb{Q})=0 \quad\text{for } i<\operatorname{rk}({\mathcal{G}}).$$

This conjecture extends known top-degree vanishing results for several Chevalley types over Euclidean number rings to a range of degrees below the virtual cohomological dimension. The source attributes it to Brück, Santos Rego, and Sroka and explains that non-vanishing results restrict such vanishing to principal ideal domains; the general conjecture remains unresolved.