On tamely ramified Iwasawa modules for the cyclotomic Z_p-extension of abelian fields

Details On tamely ramified Iwasawa modules for the cyclotomic Z_p-extension of abelian fields On tamely ramified Iwasawa modules for the cyclotomic Z_p-extension of abelian fields

2011-08-22

arxiv.org/abs/1108.4266v1

Mathematics

Number Theory

Scientific paper

Let p be an odd prime, and k_\infty the cyclotomic Z_p-extension of an abelian field k. For a finite set S of rational primes not including p, we will consider the maximal S-ramified abelian pro-p extension M_S(k_\infty) over k_\infty. We shall give a formula of the Z_p-rank of Gal(M_S(k_\infty)/k_\infty). In the proof of this formula, we also show that M_{q}(k_\infty)/L(k_\infty) is a finite extension for every real abelian field k and every rational prime q distinct from p, where L(k_\infty) is the maximal unramified abelian pro-p extension over k_\infty.

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