Some bounds for ramification of p^n-torsion semi-stable representations

Abstract : Let p be an odd prime, K a finite extension of Q_p , G_K = Gal(Kbar/K) its absolute Galois group and e = e(K/Q_p) its absolute ramification index. Suppose that T is a p^n-torsion representation of G_K that is isomorphic to a quotient of G_K -stable Z_p -lattices in a semi-stable representation with Hodge-Tate weights in {0, ..., r}. We prove that there exists a constant mu depending only on n, e and r such that the upper numbering ramification group G_K^(mu) acts on T trivially.
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Xavier Caruso, Tong Liu. Some bounds for ramification of p^n-torsion semi-stable representations. Journal of Algebra, Elsevier, 2011, 325, pp.70-96. ⟨10.1016/j.jalgebra.2010.10.005⟩. ⟨hal-00294978v2⟩

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