Tunisian Journal of Mathematics

Tame multiplicity and conductor for local Galois representations

Colin J. Bushnell and 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 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).

Article information

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

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

Permanent link to this document
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

Subjects
Primary: 11S15: Ramification and extension theory 11S37: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50] 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
Local field tame multiplicity conductor bound primitive representation

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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