5 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 $\pi:\mathfrak{X}\to S$ 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…

Let $f^\circ:X^\circ\to Y^\circ$ be a smooth family of complex projective curves of genus at least $2$, where $Y^\circ$ is one of $\mathbb{P}^1$, $\mathbb{C}$, $\mathbb{C}^*$, or a…

Let $\pi:X\to B$ be a flat family of projective curves over a projective curve $B$ with connected fibers, let $X$ have at worst quotient singularities, and let $D\subset X$ be a re…

Let $\pi:X\to B$ be a flat family of projective curves over a projective curve $B$ with connected fibers. Suppose that $X$ has at worst quotient singularities. Let $X_b$ be a gener…