3 problems

Let $M$ be a pure simple motive over $\mathbf Q$ of weight $w\leqslant -1$, with $M\neq\mathbf Q(m)$ for every $m\in\mathbf Z$. Let $V$ be its semistable $p$-adic realization and l…

Let $M/\mathbf Q$ be a pure motive of weight $\leqslant -1$ which does not contain submotives of the form $\mathbf Q(m)$. Let $V$ be its $p$-adic realisation satisfying conditions…

Let $K\in\mathcal{F}$ be unramified outside a finite set of places $\Sigma$, with the preceding critical-motive data: a full Galois-stable lattice $T$, its dual lattice $\hat T$, t…