Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

Levin, Aaron

Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 2, pp. 485-499.

Nous étudions la construction et le comptage, pour tout couple d’entiers $m,n>1$, des corps de nombres de degré $n$ dont le groupe des classes possède un “grand” $m$-rang. Notre technique repose essentiellement sur le théorème d’irréductibilité de Hilbert et sur des résultats concernant les points entiers de degré borné sur des courbes.

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 relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.

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