6 problems

Unique compatible block decomposition conjecture. The valuation data of $O/K$ admits a unique compatible block decomposition.

Symplectic equivariance conjecture. The action of $\operatorname{Sp}(6,2)$ on $\operatorname{PGL}_3(\overline{K})$-equivalence classes of Cayley octads commutes with the map $d_K$.

Octad picture stable-reduction conjecture. The stable reduction type, including whether or not it is hyperelliptic, of any smooth plane quartic over any non-archimedean local field…

Multiplicity-independence conjecture. The multiplicity of the building blocks does not affect the stable reduction, although it does affect arithmetic invariants, as in the case of…

Cayley octad valuation-data reduction conjecture. The valuation data of $O$ determines the stable reduction type of $C/K$.

Cayley octad combinatorial reduction conjecture. Combinatorial data about the configuration of these eight points fully determines the stable reduction type of the curve, analogous…