8 problems

Pappas–Rapoport's conjecture. The scheme $W$ is reduced.

Let $G$ be a complex semisimple group and let $\mu\leq\lambda$ be dominant coweights. Write $\mathcal{G}r_\mu^\lambda=\mathcal{G}r_\mu\cap\overline{\mathcal{G}r^\lambda}$ for the t…

Let $\Pi_{\bf J}$ be the global positroid variety defined by the relations of Proposition, with fiber $\Pi_{\bf J}(\veps)$ over each value of $\veps$, and let…

Let $V$) be a finite-dimensional vector space, and let $\Upsilon^{i,d-i}$ denote the corresponding catalecticant map; write $\operatorname{Minors}_r(\Upsilon^{i,d-i})$ for the idea…

Let $k$ be a finitely generated field of characteristic $0$. Let $\operatorname{Sch}^{\mathrm{ft}}_k$ be the category of finite type $k$-schemes, and let…

Very-flatness conjecture. Every flat morphism of finite type between Noetherian schemes is very flat.

Prolongation intersection conjecture.

Claw-tree intersection conjecture. The varieties associated with large claw trees are scheme-theoretic intersections of varieties associated with trees of smaller valency.