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 .
"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