## Tunisian Journal of Mathematics

### Tame multiplicity and conductor for local Galois representations

#### 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 $WF$ of $F$ and $sw(σ)$ the Swan exponent of $σ$. Assume $sw(σ)≥1$. Let $ℐF$ be the inertia subgroup of $WF$ and $PF$ the wild inertia subgroup. There is an essentially unique, finite, cyclic group $Σ$, of order prime to $p$, such that $σ(ℐF)=Σσ(PF)$. In response to a query of Mark Reeder, we show that the multiplicity in $σ$ of any character of $Σ$ is bounded by $sw(σ)$.

#### Article information

Source
Tunisian J. Math., Volume 2, Number 2 (2020), 337-357.

Dates
Revised: 8 May 2019
Accepted: 27 May 2019
First available in Project Euclid: 13 August 2019

https://projecteuclid.org/euclid.tunis/1565661719

Digital Object Identifier
doi:10.2140/tunis.2020.2.337

Mathematical Reviews number (MathSciNet)
MR3990822

Zentralblatt MATH identifier
07119007

#### Citation

Bushnell, Colin J.; Henniart, Guy. Tame multiplicity and conductor for local Galois representations. Tunisian J. Math. 2 (2020), no. 2, 337--357. doi:10.2140/tunis.2020.2.337. https://projecteuclid.org/euclid.tunis/1565661719

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