2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63006Let A be a complete discrete valuation ring with possibly imperfect residue field, and let $χ$ be a one-dimensional Galois representation over A. I show that the non-logarithmic variant of Kato's Swan conductor is the same for $χ$ and the pullback of $χ$ to the generic residual perfection of A. This implies the conductor from "Conductors and the moduli of residual perfection" (math.NT/0112305) extends the non-logarithmic variant of Kato's.15 pages. Typos correctedNumber TheoryAlgebraic Geometry11S15 (Primary) 14B99 (Secondary)text