Galois module structure of pth-power classes of cyclic extensions of degree pn

• Autores: Ján Minác, Andrew Schultz, John Swallow
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 92, Nº 2, 2006, págs. 307-341
• Idioma: inglés
• DOI: 10.1112/s0024611505015479
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• Resumen

  • In the mid-1960s Borevi$\setminus$v\{c\} and Faddeev initiated the study of the Galois module structure of groups of \$p\$th-power classes of cyclic extensions \$K/F\$ of \$p\$th-power degree. They determined the structure of these modules in the case when \$F\$ is a local field. In this paper we determine these Galois modules for all base fields \$F\$.