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On a ramification bound of semi-stable torsion representations over a local field
| Title: | On a ramification bound of semi-stable torsion representations over a local field |
| Authors: | Hattori, Shin Browse this author |
| Issue Date: | 16-Jul-2008 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 917 |
| Start Page: | 1 |
| End Page: | 30 |
| 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 $r<p-1$. Let $V$ be a semi-stable $p$-adic $G_K$-representation with Hodge-Tate weights in $\{0,\dots,r\}$. In this paper, we prove the upper numbering ramification group $G_{K}^{(j)}$ for $j>u(K,r,n)$ acts trivially on the mod $p^n$ representations associated to $V$, where $u(K,0,n)=0$, $u(K,1,n)=1+e(n+1/(p-1))$ and $u(K,r,n)=1-p^{-n}e(K(\zeta_p)/K)^{-1}+e(n+r/(p-1))$ for $r>1$. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69724 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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