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On the Ideal Class Group Problem for Global Fields

✍ Scribed by Marc Perret

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 116 KB
Volume: 77
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2366

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that any finite abelian group is the ideal class group of the ring of S-integers of some global field of given characteristic.

1999 Academic Press

Nous prouvons que tout groupe abe lien fini est groupe des classes d'ide aux de l'anneau des S-entiers d'un corps global de caracte ristique donne .

1999 Academic Press

Theorem 1. Let G be a finite abelian group. Then there exist a number field K and a finite set S of places containing the archimedian one, such that G is equal to the ideal class group Cl(O K, S ) of the ring of S-integers O S of K.

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