✦ LIBER ✦

Galois action on class groups

✍ Scribed by Franz Lemmermeyer

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 128 KB
Volume: 264
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00122-4

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✦ Synopsis

It is well known that the Galois group of an extension L/F puts constraints on the structure of the relative ideal class group Cl(L/F ). Explicit results, however, hardly ever go beyond the semisimple abelian case, where L/F is abelian (in general cyclic) and where (L : F ) and #Cl(L/F ) are coprime. Using only basic parts of the theory of group representations, we give a unified approach to these as well as more general results.

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