Conductors in the Non-Separable Residue Field Case

Abstract

Using the technique of Explicit Brauer Induction an integer-valued conductor homomorphism is constructed for Galois representations of complete, discrete valuation fields. In the special case in which the residue field extension is separable the new conductor coincides with the classical Swan conductor. In the one-dimensional case the new conductor coincides with the abelian conductor of K.Kato. In the non-separable residue field case the problem of making such a conductor was posed by J-P.Serre in 1960, motivated by the need for a generalisation of the Swan representation of a curve to higher-dimensional varieties in characteristic p.