2 problems

Hard Lefschetz-type conjecture. For every $\ell\neq p$ in the $\mathbb Q_\ell$ case, respectively for all but finitely many $\ell\neq p$ in the $\mathbb F_\ell$ and…

Let $X$ be a strictly semistable scheme over ${\mathcal O}$, and let $\Gamma_{1,K}$ and $\Gamma_{2,K}$ be correspondences on $X_K$. Write $\Gamma_K=\Gamma_{2,K}\circ\Gamma_{1,K}$,…