3 problems

Let $(K,v)$ be an algebraically maximal valued field with divisible value group and perfect residue field $k$. A field is called geometrically $C_1$ if every smooth projective sepa…

Let $(K,v)$ be an algebraically maximal valued field with divisible value group and perfect residue field $k$. A field is geometrically $C_1$ if every smooth projective separably r…

Let $k$ be a field of characteristic $0$ that is $C_1$, meaning that every hypersurface of degree at most $n$ in $\mathbb{P}^n_k$ has a $k$-rational point. Let $X$ be a terminal…