Algebraic Geometry
Stability and locally exact differentials on a curve
Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 869-872.

We show that the locally free sheaf B 1 F * (Ω X 1 ) of locally exact differentials on a smooth projective curve of genus g⩾2 over an algebraically closed field k of characteristic p is a stable bundle. This answers a question of Raynaud.

Soit X une courbe propre, lisse, connexe, de genre g, définie sur un corps k algébriquement clos de caractéristique p>0. Soit F:XX le Frobenius absolu et B 1 F * (Ω X 1 ), le faisceau des formes différentielles localement exactes sur X. C'est un fibré vectoriel sur X de rang p−1. Nous montrons qu'il est stable pour g⩾2.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.02.019
Joshi, Kirti 1

1 Math. Department, University of Arizona, 617 N Santa Rita, Tucson, AZ 85721-0089, USA
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Joshi, Kirti. Stability and locally exact differentials on a curve. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 869-872. doi : 10.1016/j.crma.2004.02.019. http://www.numdam.org/articles/10.1016/j.crma.2004.02.019/

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