Some Algebras Associated to Automorphisms of Elliptic Curves

  • Michael Artin
  • John Tate
  • M. Van den Bergh
Part of the Progress in Mathematics book series (MBC)


The main object of this paper is to relate a certain type of graded algebra, namely the regular algebras of dimension 3, to automorphisms of elliptic curves. Some of the results were announced in [V]. A graded algebra A is called regular if it has finite global dimension, polynomial growth, and is Gorenstein. The precise definitions are reviewed in Section 2. As was shown in [A-S], there are two basic possibilities for a regular algebra A of (global) dimension 3 which is generated in degree 1. Either A can be presented by 3 generators and 3 quadratic relations, or else by 2 generators and 2 cubic relations. Throughout this paper, A will denote an algebra so presented, over a ground field k.


Exact Sequence Irreducible Component Elliptic Curf Homogeneous Element Hilbert Function 


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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • Michael Artin
    • 1
  • John Tate
    • 2
  • M. Van den Bergh
    • 3
  1. 1.Dept. of MathematicsMITCambridgeUSA
  2. 2.Dept. of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Dept. Wisk. en Inform.UIAWilrijkBelgium

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