The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings

J. Bell, D. Rogalski, S. J. Sierra

Research output: Contribution to journalArticlepeer-review

Abstract

Given a projective scheme X over a field k, an automorphism sigma : X -> X, and a sigma-ample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B( X, L, sigma), 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 the primitive ideals of B are characterized by the usual Dixmier-Moeglin conditions whenever dim X <= 2.

Original languageEnglish
Pages (from-to)461-507
Number of pages47
JournalIsrael journal of mathematics
Volume180
Issue number1
DOIs
Publication statusPublished - Dec 2010

Keywords

  • LAURENT POLYNOMIAL-RINGS
  • PRIMITIVE-IDEALS
  • NOETHERIAN ALGEBRAS
  • MAPS

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