Some bounds for ramification of pn-torsion semi-stable representations

Let p be an odd prime, K a finite extension of Qp, its absolute Galois group and e=e(K/Qp) its absolute ramification index. Suppose that T is a pn-torsion representation of GK that is isomorphic to a quotient of GK-stable Zp-lattices in a semi-stable representation with Hodge–Tate weights {0,…,r}. We prove that there exists a constant μ depending only on n, e and r such that the upper numbering ramification group acts on T trivially.