Tong Liu (UPenn)

Title: A bound on ramification of pⁿ-torsion semistable representations

Abstract: Let p be an odd prime, K a p-adic field with absolute ramification index e, and T a pⁿ-torsion semi-stable representation over K with Hodge-Tate weights in {0,..., r} in the sense that T is killed by pⁿ and T can be written as a quotient of lattices in a semi-stable representation over K with Hodge-Tate weights in {0, ..., r}. We prove there exists an explicit constant c only depending on e, r and n such that the ramification group G^(c) acts on T trivially.