3 problems

Let $K$ be a complete discrete valued field with equal characteristic $0$, and let $\mathcal{X}$ be a uniruled variety over $K$. Say that a proper geometrically integral smooth $K$…

Let $K$ be a complete discrete valued field with equal characteristic $0$, and let $\mathcal{X}$ be a smooth proper integral variety of dimension $n$ over $K$. Write…

Let $k$ be a valued field, let $\mathfrak X$ be locally of the form $\operatorname{Spf}(\mathcal A^\circ)$ for $k$-affinoid algebras $\mathcal A$, so that $\mathfrak X$ is of finit…