For any -module and any , let
Let denote a separable closure of and
suppose is a (continuous)
-module.
(Note - if has characteristic , then a separable
closure is the same thing as an algebraic closure.)
For any subfield
that contains ,
let .
Let
One can prove (see [Cp86, Ch. V]) that changing the choice of separable closure only changes by unique isomorphism, i.e., the construction is essentially independent of the choice of seperable closure.
William 2007-05-25