On the number of rational points on Prym varieties over finite fields

Yves Aubry (1, 2) , Safia Haloui (3)

1 IML - Institut de mathématiques de Luminy
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 Department of Mathematics (Kongens Lyngby, Denmark)

We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.

Mots clés: Jacobians; Prym varieties; number of rational points; Abelian varieties over finite fields; number of rational points.

Domaines: Géométrie algébrique [math.AG]

Yves Aubry, Safia Haloui. On the number of rational points on Prym varieties over finite fields. Glasgow Mathematical Journal, 2016, 58 (Issue 1), pp.55--68. ⟨10.1017/S0017089515000063⟩. ⟨hal-00843686⟩