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 language | English |
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Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Mathematische Annalen |
Volume | 329 |
Issue number | 1 |
DOIs | |
Publication status | Published - May 2004 |
Externally published | Yes |