7 problems

Compatible-splitting conjecture. For any diagram $D$ and any Weyl group elements $u_1,\ldots,u_r$, the pairs

Achinger–Zdanowicz conjecture. There is a flat deformation of $X$ over the Witt vectors $W(k)$, not only over $W_2(k)$.

Let $G=\operatorname{GL}_n$, let $P$ be a parabolic subgroup containing the Borel subgroup $B$, and let $\mathfrak{u}_P$ be the nilpotent radical of the Lie algebra of $P$. Conside…

Let $X$ be a complex Abelian variety, or more generally a log Calabi–Yau variety. A complex variety has dense $F$-split type if, for a model over a finitely generated $\bZ$-algebra…

Frobenius split type conjecture. If $X$ is a log Calabi–Yau variety of characteristic zero, then $X$ has Frobenius split type.

Globally F-regular type implies log Fano. A projective globally F-regular type variety of characteristic zero is log Fano.

Let $k$ be an algebraically closed field of positive characteristic $p$. Let $V$ be a rational projective homogeneous space, set $X=V\times V$, and let $\widetilde{X}$ be the blow-…