The map V -> V//G need not be separable

Ben Martin and Amnon Neeman

Abstract. 
We construct a vector space $V$ with a linear action of a 
reductive group $G$ such that the quotient map $V \rightarrow
V//G$ (in the sense of geometric invariant theory) fails to
be separable. This gives a counterexample to an assertion of
Bardsley and Richardson.