Galois covers of ℙ1 and number fields with large class groups

Jean Gillibert (1) , Pierre Gillibert

1 IMT - Institut de Mathématiques de Toulouse UMR5219

For each finite subgroup G of PGL2(Q), and for each integer n coprime to 6, we construct explicitly infinitely many Galois extensions of Q with group G and whose ideal class group has n-rank at least #G−1. This gives new n-rank records for class groups of number fields.

Mots clés: Ideal class groups; Picard groups; cyclic fields

Domaines: Mathématiques [math]

Jean Gillibert, Pierre Gillibert. Galois covers of ℙ1 and number fields with large class groups. International Journal of Number Theory, 2022, 18 (06), pp.1261-1288. ⟨10.1142/S1793042122500646⟩. ⟨hal-03920398⟩