8 problems

Finiteness conjecture. The fundamental group $\pi_1(M_\mathrm{reg})$ is finite.

Let $f:X\to S$ be a $K$-trivial fiber space, meaning a normal $\mathbb Q$-factorial klt pair $(X,\Delta)$ endowed with a proper surjective morphism with connected fibres such that…

A primitive symplectic variety is a normal compact Kähler variety with symplectic singularities whose smooth locus carries a symplectic form and whose reflexive powers of the canon…

Finiteness conjecture. The group $\pi_1(X^{\mathrm{reg}})$ is finite:

Generalized abundance for symplectic varieties. Then $L$ is semiample.

Supersingularity conjecture. If $X$ is second-Artin supersingular, then:

Section property conjecture. This algebra epimorphism admits a multiplicative section whose image contains all Chern classes of the tangent bundle of $X$.

Decomposition conjecture. There exists a quasi-étale cover $Y \to X$ such that either $Y$ is an abelian variety, or $Y$ splits as a product of copies of a single Calabi–Yau variety…