Ramification estimate for Fontaine-Laffaille Galois modules

Suppose $K$ is unramified over ${\mathbb{Q}}_p$ and $\Gamma _K=\operatorname{Gal}(\bar K/K)$\mathrm{.}Let$H$beatorsion$\Gamma _K$-equivariant subquotient of crystalline ${\mathbb{Q}}_p[{\mathrm{\Gamma }}_K]$-module with HT weights from $[0,p-2]$. We give a new proof of Fontaine’s conjecture about the triviality of action of some ramification subgroups ${\mathrm{\Gamma }}_K^{(v)}$ on $H$. The earlier author’s proof from [1] contains a gap and proves this conjecture only for some subgroups of index $p$ in ${\mathrm{\Gamma }}_K^{(v)}$.