4 problems

Let $G$ be a reductive group over $E$, let $\operatorname{Bun}_G$ be the moduli stack of $G$-bundles on the relevant Fargues–Fontaine curve, and let $B(G)$ be the set of Kottwitz c…

Let $S\in\operatorname{Perf}_{\mathbb{F}_q}$ and let $\mathscr{E}$ be a $G$-bundle on $X_S$. Let $B$ be a Borel subgroup of $G$, and consider the moduli space of reductions of…

Let $G$ be a reductive group, let $\Gamma=\operatorname{Gal}(\overline{E}/E)$, and let $\pi_1(G)_\Gamma$ be the coinvariants of Borovoi's fundamental group. The Kottwitz map gives…

Let $E=\mathbb{F}_q((\pi))$, let $F$ be algebraically closed, and let $G$ be the reductive group considered in the paper. For $b\in G(L)$, let $\mathscr{E}_b$ be the associated $G$…