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

Xavier Caruso (1) , Tong Liu (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DRL - David Rittenhouse Laboratory

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.

Mots clés: p-adic representations; ramification

Domaines: Théorie des nombres [math.NT]

Xavier Caruso, Tong Liu. Some bounds for ramification of p^n-torsion semi-stable representations. 2008. ⟨hal-00294978v1⟩