5 problems

Curve-topology independence conjecture. The topologies $\tau_1$ and $\tau_2$ induce independent topologies on $C(K)$.

T-henselian approximation conjecture. If $\tau_1$ is t-henselian, then $\tau_1$ and $\tau_2$ induce independent topologies on $C(K)$.

Let $R$ be a $W_n$-ring on an algebraically closed field. Wn-ring conjecture. The ring $R$ is NTP$_2$, and the burden of $R$ is at most $n$. The source gives no further context or…

Let $K$ be a perfect field of positive characteristic, and let $\tau$ be a $W_n$-topology on $K$. Positive-characteristic decomposition conjecture. The topology $\tau$ is generated…

Let $(K,\tau)$ be a $W$-topological field of characteristic $0$. Decomposition conjecture. The topology $\tau$ is generated by jointly independent topologies $\tau_1,\ldots,\tau_n$…