Geometric Reductivity-A Quotient Space Approach

Mumford’s Geometric Invariant Theory or GIT is a major technique for finding quotients of algebraic schemes acted upon by reductive algebraic groups. It has been successful in finding solutions to moduli problems in the category of algebraic schemes. In the first edition (i.e., the 1965 edition) of Geometric Invariant Theory [13], Mumford restricted himself to algebraic schemes over fields of characteristic zero. In order to make his theory applicable over fields of arbitrary characteristic, he made the following conjecture in the Preface to the first edition of Ibid. (a conjecture subsequently proved by Haboush [5] in 1975).