Galois Cohomology and Real Algebraic Quotients Original Research Article

Let G be a reductive complex algebraic group with a real structure. If H subset of G is reductive, then the affine variety G/H possesses a finite number of inequivalent real structures which are compatible with the left action of G. We show how to distinguish these equivalence classes using NGH/H-modules. The (harder) problem or separating the equivalence classes with G-modules is related to another problem:identifying the real points of an algebraic quotient V//G that come from the realpoints of V.