2 problems

Let $S$ be the spectrum of a finite field or a henselian discrete valuation ring with finite residue field, and let $X$ be a smooth projective scheme over $S$. For an integer $n$ i…

Let $K$ be a global field, let $\mathcal{O}_S$ be a regular semilocal subring of $K$, and set $\mathcal{S}=\operatorname{Spec}(\mathcal{O}_S)$. Let $\mathcal{X}$ be a regular schem…