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2020 Tame multiplicity and conductor for local Galois representations
Colin J. Bushnell, Guy Henniart
Tunisian J. Math. 2(2): 337-357 (2020). DOI: 10.2140/tunis.2020.2.337

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 F 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(F)=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).

Citation

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Colin J. Bushnell. Guy Henniart. "Tame multiplicity and conductor for local Galois representations." Tunisian J. Math. 2 (2) 337 - 357, 2020. https://doi.org/10.2140/tunis.2020.2.337

Information

Received: 16 September 2018; Revised: 8 May 2019; Accepted: 27 May 2019; Published: 2020
First available in Project Euclid: 13 August 2019

zbMATH: 07119007
MathSciNet: MR3990822
Digital Object Identifier: 10.2140/tunis.2020.2.337

Subjects:
Primary: 11S15, 11S37, 22E50

Rights: Copyright © 2020 Mathematical Sciences Publishers

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