Geodesic
On the number of points on abelian and Jacobian varieties over finite fields
Yves Aubry 1   ; Safia Haloui 2   ; Gilles Lachaud 3
1 Institut de Mathématiques de Luminy Aix-Marseille Université and Institut de Mathématiques de Toulon Université du Sud Toulon-Var, France
2 Department of Mathematics Technical University of Denmark Lyngby, Denmark
3 Institut de Mathématiques de Luminy Aix-Marseille Université/CNRS, France
Acta Arithmetica, Tome 160 (2013) no. 3, pp. 201-241 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.
DOI : 10.4064/aa160-3-1
Keywords: upper lower bounds number points abelian varieties finite fields lower bounds specific jacobian varieties determine exact formulas maximum minimum number points jacobian surfaces

Yves Aubry  1   ; Safia Haloui  2   ; Gilles Lachaud  3

1 Institut de Mathématiques de Luminy Aix-Marseille Université and Institut de Mathématiques de Toulon Université du Sud Toulon-Var, France
2 Department of Mathematics Technical University of Denmark Lyngby, Denmark
3 Institut de Mathématiques de Luminy Aix-Marseille Université/CNRS, France 
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     author = {Yves Aubry and Safia Haloui and Gilles Lachaud},
     title = {On the number of points on abelian and {Jacobian} varieties over finite fields},
     journal = {Acta Arithmetica},
     pages = {201--241},
     year = {2013},
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     doi = {10.4064/aa160-3-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa160-3-1/}
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Yves Aubry; Safia Haloui; Gilles Lachaud. On the number of points on abelian and Jacobian varieties over finite fields. Acta Arithmetica, Tome 160 (2013) no. 3, pp. 201-241. doi: 10.4064/aa160-3-1

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