3 problems

Local constancy conjecture. If $U$ is contractible, then the restriction functor $i_u^*$ is an equivalence. This is the fiberwise formulation of local constancy for the automorphic…

Let $G$ be a reductive group, let $\check{G}$ be its Langlands dual group, and let $\operatorname{Shv}_{c,\operatorname{Nilp}}(\operatorname{Bun}_G)$ denote the category of $c$-twi…

Let $\pi:\mathfrak{X}\to S$ be the family of curves in the paper, let $\operatorname{Bun}_G(\pi_U)$ be the moduli stack of $G$-bundles on the base-changed family over a contractibl…