A note on rationality of representations of profinite groups
Let \(G\) be a profinite group. The purpose of this note is to construct subfields \(F\) of the field of complex numbers over which a given finite dimensional complex continuous linear representation \(D\) of \(G\) is realizable in the following sense: There is a one-dimensional representation \(\mu\) of \(G\) such that \(\mu D\) is isomorphic to a linear representation which is realizable over \(F\). The proofs are based on classical results on finite linear groups and on cohomological methods.
scientific article; zbMATH DE number 1186385