Ideal Class Groups and Rational Torsion in Jacobians of Curves
We study the problem of constructing and enumerating, for any integers m,
n> 1, number fields of degree n whose ideal class groups have "large"
m-rank. Our technique, which appears to be new, relies on the Hilbert
Irreducibility Theorem and finding certain curves whose Jacobians have a
large rational torsion subgroup. Using this technique we improve on
results of Nakano, Bilu-Luca, and others.