2 problems

Solubility conjecture. Every small ${\mathscr O}_{\mathfrak X}[\frac 1 p]$-Higgs bundle with coefficients in $\xi^{-1}\Omega^1_{{\mathfrak X}/{\mathscr S}}$ is soluble. This is par…

Let $(M,\theta_M,\phi_M)$ be an enhanced log Higgs module over $R[\frac{1}{p}]$, and let $V(M,\theta_M,\phi_M)$ be the associated representation of $\Gamma$. Local inverse Simpson…