# On a Ramification Bound of Torsion Semi-stable Representations over a Local Field

#### Abstract

Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac(W ) of degree e and r be a non-negative integer satisfying r < p − 1. In this paper, we prove the upper numbering ramification group G (j) K for j > u(K, r, n) acts trivially on the p-torsion semi-stable GK-representations with Hodge-Tate weights in {0, . . . , r}, where u(K, 0, n) = 0, u(K, 1, n) = 1 + e(n + 1/(p − 1)) and u(K, r, n) = 1− p + e(n + r/(p − 1)) for 1 < r < p − 1.

### Cite this paper

@inproceedings{Hattori2009OnAR, title={On a Ramification Bound of Torsion Semi-stable Representations over a Local Field}, author={Shin Hattori}, year={2009} }