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

Shin Hattori

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2474-2503
Number of pages30
JournalJournal of Number Theory
Volume129
Issue number10
DOIs
Publication statusPublished - Oct 2009

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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