Minus class groups of the fields of the <IMG ALIGN=BOTTOM >-th roots of unity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	René Schoof

Institution:	Dipartimento di Matematica, $2^{{a}}$ Università di Roma ``Tor Vergata", I-00133 Rome, Italy

Abstract:	We show that for any prime number the minus class group of the field of the -th roots of unity $\overline{\mathbf{Q}_p} (\zeta _l)$ admits a finite free resolution of length 1 as a module over the ring $\widehat{\mathbf{Z}} G]/(1+\iota)$ . Here $\iota$ denotes complex conjugation in $G={{Gal}}( \overline{\mathbf{Q}_p} (\zeta _l)/\overline{\mathbf{Q}_p} )\cong(\mathbf{Z} /l\mathbf{Z} )^*$ . Moreover, for the primes $l\le 509$ 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.

Keywords:	Cyclotomic fields class groups cohomology of groups

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