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arXiv · 0812.3355

The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings

J. Bell·D. Rogalski·S. J. Sierra
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Abstract

Given a projective scheme $X$ over a field $k$, an automorphism $σ$ of $X$, 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 the dimension of $X$ is no more than 2.

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J. Bell, D. Rogalski, S. J. Sierra. 2008-12-17. The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings. https://arxiv.org/abs/0812.3355

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