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Kato's conductor and generic residual perfection

James M. Borger
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Abstract

Let 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.

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James M. Borger. 2002-03-27. Kato's conductor and generic residual perfection. https://arxiv.org/abs/math/0112306

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