3 problems

Analytic local uniformization conjecture. Every point $x\in X^{\operatorname{ad}}$ is uniformizable.

Local uniformization conjecture. For every valuation $\nu$ of $K/k$, there exists a projective model $M$ of $K/k$ on which the foliation $\mathcal{F}$ is log-final at the center of…

Tight extension conjecture. The valuation $nu$ admits at least one tight extension $hat\nu_-$. It can be chosen so that, for rings $R'$ sufficiently far in $cal T$,