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The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings

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Abstract

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 the primitive ideals of B are characterized by the usual Dixmier-Moeglin conditions whenever dim X ≤ 2.

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Author notes

  1. S. J. Sierra

    Present address: Department of Mathematics, Princeton University Fine Hall, Washington Road, Princeton, NJ, 08544, USA

Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    J. Bell

  2. Department of Mathematics, University of California San Diego, La Jolla, CA, 92093-0112, USA

    D. Rogalski

  3. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA

    S. J. Sierra

Authors
  1. J. Bell
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  2. D. Rogalski
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  3. S. J. Sierra
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Corresponding authors

Correspondence to J. Bell or S. J. Sierra.

Additional information

Partially supported by NSERC through grant 611456.

Partially supported by the NSF through grant DMS-0600834

Partially supported by the NSF through grant DMS-0802935.

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Bell, J., Rogalski, D. & Sierra, S.J. The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings. Isr. J. Math. 180, 461–507 (2010). https://doi.org/10.1007/s11856-010-0111-0

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  • DOI: https://doi.org/10.1007/s11856-010-0111-0

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