Vector bundles of degree zero over an elliptic curve
[Fibrés vectoriels de degré zéro sur une courbe elliptique]
Lekaus, Silke1
1 FB 6 – Mathematik, Universität Essen, Universitätsstraße 3, 45117 Essen, Germany
Comptes Rendus. Mathématique, Tome 335 (2002) no. 4, pp. 351-354.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02478-0
Lekaus, Silke 1

1 FB 6 – Mathematik, Universität Essen, Universitätsstraße 3, 45117 Essen, Germany 
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Lekaus, Silke. Vector bundles of degree zero over an elliptic curve. Comptes Rendus. Mathématique, Tome 335 (2002) no. 4, pp. 351-354. doi : 10.1016/S1631-073X(02)02478-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)02478-0/

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