On a ramification bound of torsion semi-stable representations over a local field
On a ramification bound of torsion semi-stable representations over a local field
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局部场上扭转半稳定表示的分枝界
DOI：
10.1016/j.jnt.2009.04.012
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发表时间：
2008
影响因子：
0.7
通讯作者：
Shin Hattori
中科院分区：
文献类型：
--
作者：
Shin Hattori
设p是有理素数，k是特征p的完备域，W=W(K)是Witt向量环，K是e次有限完全分枝的Frc(W)，r是满足r<；p−1的非负整数.本文证明了j>；u(K，r，n)的上数分支群GK(J)平凡地作用于{0，…中具有Hodge-Tate权的pn-扭半稳定GK-表示，r}，其中u(K，0，n)=0，u(K，1，n)=1+e(n+1/(p−1))，u(K，r，n)=1−p−n+e(n+r/(p−1))，对1<；r<；p−1。
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.