Elliptic surfaces over ℙ¹ and large class groups of number fields

2018/11/20 by Gillibert, Jean, Levin, Aaron
#11R29 (Primary) 11G05 #14J27 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.08166

Abstract

Given a non-isotrivial elliptic curve over ℚ(t) with large Mordell-Weil rank, we explain how one can build, for suitable small primes p, infinitely many fields of degree p²-1 whose ideal class group has a large p-torsion subgroup. As an example, we show the existence of infinitely many cubic fields whose ideal class group contains a subgroup isomorphic to (ℤ/2ℤ)¹¹.

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