Conductors and the moduli of residual perfection

James M. Borger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Let A be a complete discrete valuation ring with possibly imperfect residue field. The purpose of this paper is to give a notion of conductor for Galois representations over A which agrees with the classical Artin conductor when the residue field is perfect. The definition rests on two results of perhaps wider interest: there is a moduli space that parametrizes the ways of modifying A so that its residue field is perfect, and any Galois-theoretic object over A can be recovered from its pullback to the (residually perfect) discrete valuation ring corresponding to the generic point of this moduli space. Finally, I show that this conductor extends the non-logarithmic variant of Kato's conductor to representations of rank greater than one.

Original languageEnglish
Pages (from-to)1-30
Number of pages30
JournalMathematische Annalen
Volume329
Issue number1
DOIs
Publication statusPublished - May 2004
Externally publishedYes

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