Tame multiplicity and conductor for local Galois representations

IF 0.8 Q2 MATHEMATICS
C. Bushnell, G. Henniart
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引用次数: 1

Abstract

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$. Let $\sigma$ be an irreducible smooth representation of the absolute Weil group $\Cal W_F$ of $F$ and $\sw(\sigma)$ the Swan exponent of $\sigma$. Assume $\sw(\sigma) \ge1$. Let $\Cal I_F$ be the inertia subgroup of $\Cal W_F$ and $\Cal P_F$ the wild inertia subgroup. There is an essentially unique, finite, cyclic group $\varSigma$, of order prime to $p$, so that $\sigma(\Cal I_F) = \sigma(\Cal P_F)\varSigma$. In response to a query of Mark Reeder, we show that the multiplicity in $\sigma$ of any character of $\varSigma$ is bounded by $\sw(\sigma)$.
局部伽罗瓦表示的驯服多重性和导体
设$F$是残差特征为$p$的非阿基米德局部紧致场。设$\sigma$是$F$的绝对Weil群$\Cal W_F$和$\sw(\sigma)$的Swan指数的不可约光滑表示。假设$\sw(\sigma)\ge1$。设$\Cal I_F$是$\Cal W_F$的惯性子群,$\Cal P_F$是野生惯性子群。存在一个本质上唯一的、有限的、循环的群$\varSigma$,其阶素数为$p$,因此$\sigma(\Cal I_F)=\s西格玛(\Cal p_F)\varSigma$。作为对Mark Reeder的查询的回应,我们证明了$\varSigma$的任何字符在$\sigma$中的多重性是由$\sw(\sigma)$限定的。
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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