Frobenius semisimplicity at the eigenvalue 1

Let $V_l^i$ be the $l$-adic representation attached to the $i$th cohomology of the generic fibre, and let $R\Gamma_f(\mathbb Q_p,V_l^i)$ be the corresponding local finite-cohomology complex. A two-term complex $C=(W\xrightarrow{\lambda}W)$ is semisimple at zero when the natural map from $H^0(C)=\ker(\lambda)$ to $H^1(C)=\operatorname{coker}(\lambda)$ is an isomorphism. Frobenius-semisimplicity conjecture. For any prime number $p$, the complex $R\Gamma_f(\mathbb Q_p,V_l^i)$ is semisimple at zero. This condition is a local semisimplicity assertion at the Frobenius eigenvalue $1$ and is introduced as a conjectural reformulation related to the Tamagawa number conjecture.