Construction and classification of some Galois modules

Details Construction and classification of some Galois modules Construction and classification of some Galois modules

2003-04-15

arxiv.org/abs/math/0304203v1

Math. Z. 250 (2005), no. 4, 907--914

Mathematics

Number Theory

Scientific paper

10.1007/s00209-005-0785-x

In our previous paper we describe the Galois module structures of $p$th-power class groups $K^\times/{K^{\times p}}$, where $K/F$ is a cyclic extension of degree $p$ over a field $F$ containing a primitive $p$th root of unity. Our description relies upon arithmetic invariants associated with $K/F$. Here we construct field extensions $K/F$ with prescribed arithmetic invariants, thus completing our classification of Galois modules $K^{\times}/K^{\times p}$.

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