紀要論文

紀要論文

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Osaka Journal of Mathematics. 2014, 51(2), p. 513-536

ON TAMELY RAMIFIED IWASAWA MODULES FOR THE CYCLOTOMIC Z_p-EXTENSION OF ABELIAN FIELDS

Itoh, Tsuyoshi

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2014-04

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

10.18910/29204

29204

ON TAMELY RAMIFIED IWASAWA MODULES FOR THE CYCLOTOMIC Z_p-EXTENSION OF ABELIAN FIELDS

Itoh, Tsuyoshi

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-04

Osaka Journal of Mathematics

51

2

513

536

https://hdl.handle.net/11094/29204

10.18910/29204

https://doi.org/10.18910/29204