Ramification estimate for Fontaine-Laffaille Galois modules

Abstract

Suppose $K$ is unramified over ${\mathbb{Q}}_p$ and ${\Gamma }_K=\mathrm{Gal}(\bar{K}/K)$. Let $H$ be a torsion ${\Gamma }_K$-equivariant subquotient of crystalline ${\mathbb{Q}}_p[{\Gamma }_K]$-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 ${\Gamma }_K^{(v)}$ on $H$. The earlier author's proof from [1] contains a gap and proves this conjecture only for some subgroups of index $p$ in ${\Gamma }_K^{(v)}$.

9 pages