Algebraic Geometry Seminar

Jim Borger (Chicago)

Conductors and the moduli of residual perfection

Let A be a complete discrete valuation ring with possibly imperfect residue field. I will propose a notion of conductor for Galois representations over A that generalizes the classical Artin conductor. The definition rests on two results of perhaps more general 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. I will also say something about how this conductor is related to Kato's refined Swan conductor, which is defined for rank-one representations.

Strictly speaking, no knowledge of algebraic geometry is required, but I will say a few words about how all this is related to algebraic geometry.