论文信息 - Minus class groups of the fields of the l-th roots of unity

Minus class groups of the fields of the l-th roots of unity

We show that for any prime number l > 2 the minus class group of the field of the l-th roots of unity Q p (ζl) admits a finite free resolution of length 1 as a module over the ring Z[G]/(1 + i). Here i denotes complex conjugation in G = Gal(Q p (ζl)/Q p ) ≅ (Z/lZ)*. Moreover, for the primes l < 509 we show that the minus class group is cyclic as a module over this ring. For these primes we also determine the structure of the minus class group.

René Schoof | R. Schoof

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