Conductors and the moduli of residual perfection
J. Borger, Conductors and the moduli of residual perfection,
Mathematische Annalen 329 (2004) No. 1, pp 1-30
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 that generalizes the
classical Artin conductor. 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 definition of conductor extends the non-logarithmic
variant of Kato's conductor to representations of rank greater than one.
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