Local \varepsilon _0-characters in torsion rings

Abstract

Let p be a rational prime and K a complete discrete valuation field with residue field k of positive characteristic p. When k is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local ε 0 -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic ≠p, of the Weil group W K of K. In this paper, we generalize the results in [10] and [11] to the case where k is an arbitrary perfect field.