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

Xavier Caruso; Tong Liu

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arXiv · 0805.4227

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

Xavier Caruso·Tong Liu

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Abstract

Let p be an odd prime, K a finite extension of Q_p, G=Gal(\bar K/K) the Galois group and e=e(K/Q_p) the ramification index. Suppose T is a p^n torsion representation such that T is isomorphic to a quotient of two G-stable Z_p-lattices in a semi-stable representation with Hodge-Tate weights in {0,...,r}. We prove that there exists a constant μexplicitly depending on n, e and r such that the upper numbering ramification group G^{(μ)} acts on T trivially.

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Xavier Caruso, Tong Liu. 2008-07-09. Some Bounds for ramification of $p^n$-torsion semi-stable representations. https://arxiv.org/abs/0805.4227

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