The Dixmier–Moeglin conjecture for twisted homogeneous coordinate rings

Let $X$ be a projective $k$-scheme of any dimension, let $\sigma:X\to X$ be an automorphism, let $\mathcal{L}$ be a $\sigma$-ample invertible sheaf, and let $B(X,\mathcal{L},\sigma)$ denote the associated twisted homogeneous coordinate ring. The Dixmier–Moeglin conjecture. The ring $B(X,\mathcal{L},\sigma)$ satisfies the Dixmier–Moeglin equivalence. The conjecture proposes the Dixmier–Moeglin equivalence for all twisted homogeneous coordinate rings arising from projective schemes and $\sigma$-ample sheaves; the supplied text gives no resolution.