The field descent and class groups of CM -fields
نویسنده
چکیده
We consider the following “field descent problem” for principal ideals I of number fields K. Assume that I is invariant under a Galois automorphism σ of K; decide wether there is a generator g of I with gσ = g, i.e., wether I can be generated by an element of Fix σ. We solve this problem for certain ideals by elementary methods. As a consequence, we are able to exhibit large explicit subgroups of class groups of CM -fields. This leads to some good lower bounds for the p-ranks of these class groups. 2000 Mathematics Subject Classification 11R29 (primary), 11R20 (secondary)
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