10 problems

Let $X$ be a simply connected smooth projective variety. Universal nonabelian mixed Hodge structure conjecture. There is a universal morphism to a simply connected nonabelian mixed…

Let ${\cal V}$ and ${\cal Y}$ be nonabelian mixed Hodge structures, and suppose that ${\cal Y}$ is $1$-connected, meaning that its $\pi_0$ and $\pi_1$ are trivial. Internal Hom con…

An analytic vector scheme is defined locally as the kernel of a map of finite-rank vector bundles. Conjecture on analytic vector schemes. This definition is equivalent to the notio…

An $n$-stack is a functor on a site satisfying descent with respect to sieves, and $nSTACK/{\cal X}$ denotes the resulting higher category of $n$-stacks. Let $U'$ be an $n$-stack w…

Let $S$ be a base scheme, let ${\cal X}/S$ be the relevant site over $S$, and let $G$ be an abelian affine presentable group sheaf on ${\cal X}/S$. Here, affine means that for ever…

Let $X$ be a finite extension of a local nonarchimedean field, and consider the rigid analytic stack constructed in the cited work of EGH. Generalized rigid analytic stack conjectu…

Let $\mathcal{X}$ be a quasi-compact fibered category over $R$, and let $\mathcal{C}$ be as in the resolution-property hypothesis of the paper. Write…

Let $n\geq 2$ be even, let $\pi^*V$ be the pullback of the vector bundle to the stack considered in the paper, and let $\mathbb{H}=\langle 1\rangle+\langle -1\rangle$ denote a hype…

Local 1-affineness conjecture. The prestack $\LocSys_\cG(\oD)$ is 1-affine.

Let ${\mathcal X}$ be a smooth Gorenstein Deligne–Mumford stack over a finite field, let $\overline{{\mathcal X}}$ denote its base change to an algebraic closure, and let…