Manin's conjecture on rational hypersurfaces over $C_1$ fields

Let $k$ be a $C_1$ field, and let $V$ be a rational hypersurface over $k$. Manin's conjecture. The hypersurface $V$ has a $k$-rational point. This is a weaker variant of Lang's conjecture and remains open; in particular, the paper states that Manin's conjecture is still open for $\Q_p^{\mathrm{ur}}$.