On the maximum number of rational points on singular curves over finite fields

Yves Aubry (1, 2) , Annamaria Iezzi (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 I2M - Institut de Mathématiques de Marseille

We give a construction of singular curves with many rational points over finite fields. This construction enables us to prove some results on the maximum number of rational points on an absolutely irreducible projective algebraic curve defined over Fq of geometric genus g and arithmetic genus π.

Mots clés: zeta function; Singular curves; finite fields; rational points

Domaines: Géométrie algébrique [math.AG]

Yves Aubry, Annamaria Iezzi. On the maximum number of rational points on singular curves over finite fields. Moscow Mathematical Journal, 2015, 15 (4), pp.615--627. ⟨10.17323/1609-4514-2015-15-4-615-627⟩. ⟨hal-01103802v2⟩