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Comptes Rendus Mathématique
Volume 335, n° 4
pages 351-354 (2002)
Doi : S1631-073X(02)02478-0
Received : 18 Mars 2002 ;  accepted : 20 June 2002
Vector bundles of degree zero over an elliptic curve
Fibrés vectoriels de degré zéro sur une courbe elliptique
 

Silke Lekaus
FB 6 - Mathematik, Universität Essen, Universitätsstraße 3, 45117 Essen, Germany 

Note presented by Jean-Pierre Serre

Abstract

In this Note we study indecomposable vector bundles of degree zero over an elliptic curve. We show that each bundle generates a ring and a Tannakian category, such that the ring and the group scheme associated to the Tannakian category are of the same dimension. Furthermore we show that the result does not extend to curves of genus 2. To cite this article: S. Lekaus, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 351-354.

The full text of this article is available in PDF format.
Résumé

Dans cette Note, nous étudions les fibrés vectoriels indécomposables de degré zéro sur une courbe elliptique. Nous montrons que chaque fibré engendre un anneau et une catégorie tannakienne tels que l'anneau et le schéma en groupes associé à la catégorie soient de la même dimension. De plus, nous montrons que ce résultat ne s'étend pas aux courbes de genre 2. Pour citer cet article : S. Lekaus, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 351-354.

The full text of this article is available in PDF format.


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