Galois covers of ℙ¹ and number fields with large class groups

2020/05/21 by Jean Gillibert, Pierre Gillibert, Gillibert, Jean +1
Mathematics · #11R29 (Primary) 11R16 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2005.10920

openalex publication_date 2020/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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