The Dixmier-moeglin Equivalence for Twisted Homogeneous Coordinate Rings

Given a projective scheme X over a field k, an automorphism σ : X → X, and a σ-ample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B(X,L, σ), one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum of B, as well as that of other closely related algebras such as skew and skew-Laurent extensions of commutative algebras. Over an algebraically closed, uncountable field k of characteristic zero, we prove that that the primitive ideals of B are characterized by the usual Dixmier-Moeglin conditions whenever