Hochster–Roberts theorem
In algebra, the Hochster–Roberts theorem, introduced by,
states that rings of invariants of linearly reductive groups acting on regular rings are Cohen–Macaulay.
In other words,
proved that if a variety over a field of characteristic 0 has rational singularities then so does its quotient by the action of a reductive group; this implies the Hochster–Roberts theorem in characteristic 0 as rational singularities are Cohen–Macaulay.
In characteristic p>0, there are examples of groups that are reductive acting on polynomial rings whose rings of invariants are not Cohen–Macaulay.
