Kato's conductor and generic residual perfection

2001/12/29 by James M. Borger, Borger, James M.
Mathematics · #11S15 (Primary) 14B99 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11S15 #msc:14B99

paper · pdf · doi:10.48550/arxiv.math/0112306

15 pages. Typos corrected

arxiv created 2002/03/27 · arxiv updated 2009/11/30

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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