Some Algebras Associated to Automorphisms of Elliptic Curves
Identifieur interne : 000948 ( Main/Merge ); précédent : 000947; suivant : 000949Some Algebras Associated to Automorphisms of Elliptic Curves
Auteurs : Michael Artin [États-Unis] ; John Tate [États-Unis] ; M. Van Den Bergh [Belgique]Source :
- Progress in Mathematics [ 2197-1803 ] ; 2007.
Abstract
Abstract: 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.
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DOI: 10.1007/978-0-8176-4574-8_3
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