TY - JOUR

T1 - On a ramification bound of torsion semi-stable representations over a local field

AU - Hattori, Shin

N1 - Funding Information:
The author would like to pay his gratitude to Iku Nakamura and Takeshi Saito for their warm encouragements. He wants to thank Manabu Yoshida for kindly allowing him to include the proof of Proposition 5.6. He also wants to thank Ahmed Abbes, Xavier Caruso, Takeshi Tsuji, and especially Victor Abrashkin and Yuichiro Taguchi, for useful discussions and comments. Finally, he is very grateful to the referee for his or her valuable comments to improve this paper. This work was partially supported by 21st Century COE program “Mathematics of Nonlinear Structure via Singularity” at Department of Mathematics, Hokkaido university, and by the JSPS International Training Program (ITP).

PY - 2009/10

Y1 - 2009/10

N2 - Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac (W) of degree e and r be a non-negative integer satisfying r < p - 1. In this paper, we prove the upper numbering ramification group GK(j) for j > u (K, r, n) acts trivially on the pn-torsion semi-stable GK-representations with Hodge-Tate weights in {0, ..., r}, where u (K, 0, n) = 0, u (K, 1, n) = 1 + e (n + 1 / (p - 1)) and u (K, r, n) = 1 - p- n + e (n + r / (p - 1)) for 1 < r < p - 1.

AB - Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac (W) of degree e and r be a non-negative integer satisfying r < p - 1. In this paper, we prove the upper numbering ramification group GK(j) for j > u (K, r, n) acts trivially on the pn-torsion semi-stable GK-representations with Hodge-Tate weights in {0, ..., r}, where u (K, 0, n) = 0, u (K, 1, n) = 1 + e (n + 1 / (p - 1)) and u (K, r, n) = 1 - p- n + e (n + r / (p - 1)) for 1 < r < p - 1.

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U2 - 10.1016/j.jnt.2009.04.012

DO - 10.1016/j.jnt.2009.04.012

M3 - Article

AN - SCOPUS:67650451370

VL - 129

SP - 2474

EP - 2503

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 10

ER -