3 problems

Let $K$ be a number field, let $G$ be a finite group, and let $\mathcal X=BG_K$. Let $c$ be the raising function on the connected components of the relevant inertia stack, and defi…

Let $K$ be a number field, let $G$ be a constant group scheme over $K$, and let $\mathcal{X}=BG_{\mathcal O_K}$ be equipped with a vector bundle $\mathcal V$. For an open substack…

Let $k=\mathbb C$, and for every prime $p\geq 3$ let $G_p$ be the Heisenberg group of order $p^3$. Write $\{B_{\mathbb C}G_p\}$ for the motivic class of its classifying stack and…