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Journal de Th´

eorie des Nombres

de Bordeaux

19

(2007), 485–499

Ideal class groups, Hilbert’s irreducibility

theorem, and integral points of bounded degree

on curves

par

Aaron LEVIN

R´esum´e. Nous ´etudions la construction et le comptage, pour tout couple d’entiersm, n >1, des corps de nombres de degr´endont le

groupe des classes poss`ede un “grand”m-rang. Notre technique

repose essentiellement sur le th´eor`eme d’irr´eductibilit´e de Hilbert et sur des r´esultats concernant les points entiers de degr´e born´e sur des courbes.

Abstract. We study the problem of constructing and enumer-ating, for any integersm, n >1, number fields of degreenwhose

ideal class groups have “large”m-rank. Our technique relies

fun-damentally on Hilbert’s irreducibility theorem and results on in-tegral points of bounded degree on curves.

AaronLevin

Centro di Ricerca Matematica Ennio De Giorgi Collegio Puteano

Scuola Normale Superiore Piazza dei Cavalieri, 3 I-56100 Pisa, Italy

E-mail:[email protected]

Referensi

Unduh sekarang ( PDF - 1 Halaman - 53.80 KB )

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