Comptes Rendus
Algebraic Geometry
On vector bundles on curves over F¯p
Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 213-216.

Let V be a vector bundle over an irreducible smooth projective curve defined over the field F¯p. For any integer r(0,rank(V)), let Grr(V) be the Grassmann bundle parametrizing r-dimensional quotients of the fibers of V. Let L be a line bundle over Grr(V) such that LC>0 for every irreducible closed curve CGrr(V). We prove that L is ample.

Soit V un fibré vectoriel sur une courbe projective lisse irréductible définie sur F¯p. Pour tout entier r(0,rank(V)), soit Grr(V) le fibré en grassmanniennes paramétrisant les quotients de dimension r des fibrés de V. Soit L un fibré en droites sur Grr(V) tel que LC>0 pour toute courbe fermée irréducible CGrr(V). On prouve alors que L est ample.

Published online:
DOI: 10.1016/j.crma.2012.01.006

Indranil Biswas 1; A.J. Parameswaran 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
     author = {Indranil Biswas and A.J. Parameswaran},
     title = {On vector bundles on curves over $ {\overline{\mathbb{F}}}_{p}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {213--216},
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     year = {2012},
     doi = {10.1016/j.crma.2012.01.006},
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Indranil Biswas; A.J. Parameswaran. On vector bundles on curves over $ {\overline{\mathbb{F}}}_{p}$. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 213-216. doi : 10.1016/j.crma.2012.01.006.

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