Quantitative Riemann existence theorem over a number field

Yuri Bilu (1) , Marco Strambi (1)

1 IMB - Institut de Mathématiques de Bordeaux

Given a covering of the projective line with ramifications defined over a number field, we define a plain model of the algebraic curve realizing the Riemann existence theorem for this covering, and bound explicitly the defining equation of this curve and its definition field.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Yuri Bilu, Marco Strambi. Quantitative Riemann existence theorem over a number field. Acta Arithmetica, 2010, 145 (4), pp.319-339. ⟨10.4064/aa145-4-2⟩. ⟨hal-00383076⟩