10 problems

Let $X$ be a smooth complete curve, let $G$ be a reductive group, and let $\Bun_G$ be the moduli stack of principal $G$-bundles on $X$. Write $\Shv_{\Nilp}(\Bun_G)$ for the subcate…

Let $G$ be the group in the paper, let $P$ be a standard proper parabolic with Levi subgroup $M$, and let $W$ be an irreducible local system on $X$ of rank $r=\dim V^\gamma$. For…

Let $X$ be the curve and $G$ the reductive group of the paper. Let $E$ be a $\check{G}$-local system on $X$, and put $W=V^{\gamma}_E$. Assume that $W$ is irreducible and that whene…

Let $X$ be the underlying smooth projective curve, let $\bar R$ be the coefficient ring with local homomorphism $\bar R\to\mathcal O$, and let $\bar E$ be a smooth $\bar R$-sheaf o…

Let $E$ be the local field underlying the Weil group $W_E$, let $G=\mathrm{GL}_n$, and let $B(G)$ denote its Kottwitz set. Write $\mathrm{Bun}_n$ for the moduli stack of $G$-bundle…

The subregular Arthur-sheaf conjecture. If $\operatorname{char}(k)\neq 2$ or $3$, then there exists a unique sheaf $\mathcal F_{\mathrm{sr}}$ on $\operatorname{Bun}_G$ such that, o…

Let $G$ be the reductive group under consideration, let $X$ be the underlying curve, and let $\check{G}$ be its Langlands dual group. Let … be a distinguished unipotent Arthur para…

In the situation of Theorem, let $F_G(K_{E,\chi, \mathbb H})$ be the complex on $\operatorname{Bun}_{\mathbb G}$ constructed there, and let $\Whit$ denote the first Whittaker coeff…

Let $X$ be a smooth projective curve and let $E$ be an irreducible $\operatorname{SL}_2$-local system on $X$. Assume Lyubashenko's Conjecture 3 holds for the point…

Let $\operatorname{Bun}_H$ be the stack of $H$-bundles, let ${\cal K}_H$ be the perverse sheaf constructed in the paper, and let ${\cal C}^0\subset T^*\operatorname{Bun}_H$ be the…