Tunisian Journal of Mathematics
- Tunisian J. Math.
- Volume 2, Number 2 (2020), 337-357.
Tame multiplicity and conductor for local Galois representations
Let be a non-Archimedean locally compact field of residual characteristic . Let be an irreducible smooth representation of the absolute Weil group of and the Swan exponent of . Assume . Let be the inertia subgroup of and the wild inertia subgroup. There is an essentially unique, finite, cyclic group , of order prime to , such that . In response to a query of Mark Reeder, we show that the multiplicity in of any character of is bounded by .
Tunisian J. Math., Volume 2, Number 2 (2020), 337-357.
Received: 16 September 2018
Revised: 8 May 2019
Accepted: 27 May 2019
First available in Project Euclid: 13 August 2019
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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