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arXiv · 1809.05666

Tame multiplicity and conductor for local Galois representations

Colin J. Bushnell·Guy Henniart
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Abstract

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$. Let $σ$ be an irreducible smooth representation of the absolute Weil group $\Cal W_F$ of $F$ and $\sw(σ)$ the Swan exponent of $σ$. Assume $\sw(σ) \ge1$. 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 $σ(\Cal I_F) = σ(\Cal P_F)\varSigma$. In response to a query of Mark Reeder, we show that the multiplicity in $σ$ of any character of $\varSigma$ is bounded by $\sw(σ)$.

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Colin J. Bushnell, Guy Henniart. 2019-05-08. Tame multiplicity and conductor for local Galois representations. https://doi.org/10.2140/tunis.2020.2.337

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