2 problems

Let $X=(\mathbb{C}^*)^n\subset\mathbb{C}^{n+1}$. A normal crossings divisor in $\mathbb{P}^n$ is the union of $n+1$ hyperplanes in general position. The categorical intersection co…

Let $K$ be a number field with ring of integers $\mathcal{O}_K$, let $S$ contain the archimedean places, and let $\mathscr{X}\to\operatorname{Spec}\mathcal{O}_{K,S}$ be a smooth pr…