16 problems

Let $C$ be a smooth projective curve over an algebraically closed field of characteristic $p$, and consider the moduli space of semistable parabolic bundles of rank $2$ on $C$ with…

Hara–Watanabe's conjecture. Divisorially F-regular pairs correspond to plt singularities.

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

Large-characteristic quasi-$F^{\infty}$-splitting conjecture. There exists an integer $p_d>0$ such that, if $p>p_d$, every smooth proper quasi-$F$-split $K$-trivial variety of dime…

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…

Equality of test ideals conjecture. All versions of test ideals in tight closure theory should be equal.

Locally sharply Frobenius split type conjecture. If $(X,Delta)$ is log canonical, then it is of locally sharply Frobenius split type.

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-…

Module-valued lower semicontinuity conjecture. The function $s_{e,M}$ is lower semicontinuous.

Lower semicontinuity conjecture. The function $s_e:\operatorname{Spec}(R)\to\mathbb{Q}$ is lower semicontinuous.

Dimension-function conjecture. The equivalence relation induced on ${\mathcal Y}_{\operatorname{init} f}$ by $\pi_{f,\operatorname{init}}$ can be determined from this function as t…

Let $Z=G/P\times G/P$, where $G/P$ is a rational homogeneous variety, and let the diagonal copy of $G/P$ be the subvariety of $Z$. A splitting of $Z$ is a section of $K_Z^{1-p}$ de…