3 problems

Nagai's conjecture. The monodromy operators satisfy

Fix a prime $p$, let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field, and let $X$ be a hyper-Kähler variety over $K$ of dimensi…

Let $\mathcal{X}$ be a smooth algebraic orbifold with coarse moduli space $|\mathcal{X}|$, and suppose there is a crepant resolution $Y\to |\mathcal{X}|$ such that $Y$ is hyper-Käh…