Ramification estimate for Fontaine–Laffaille Galois modules

Suppose K   is unramified over QpQp and ΓK=Gal(K¯/K). Let H   be a torsion ΓKΓK-equivariant subquotient of crystalline Qp[ΓK]Qp[ΓK]-module with HT weights from [0,p−2][0,p−2]. We give a new proof of Fontaine's conjecture about the triviality of action of some ramification subgroups ΓK(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 ΓK(v).