2 problems

Refined Colmez conjecture. There exists an integer $m\geq1$ and an element $\beta=\beta(A,m,\phi)\in\omega_{\cal A}^{\otimes m}$ such that (a) $\beta$ generates…

Assume that $\dim X=1$. Let $P$ be the weight group of $\Delta_{\hat\Pi}$, let $Q\subset P$ be the subgroup generated by the roots, and let…