ON THE ℤ<sub>p</sub>-RANKS OF TAMELY RAMIFIED IWASAWA MODULES

DOI DOI Web Site 被引用文献3件 オープンアクセス
  • TSUYOSHI ITOH
    Division of Mathematics, Education Center, Faculty of Social Systems Science, Chiba Institute of Technology, 2-1-1 Shibazono, Narashino, Chiba 275-0023, Japan
  • YASUSHI MIZUSAWA
    Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466-8555, Japan
  • MANABU OZAKI
    Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan

説明

<jats:p> For a finite set S of prime numbers, we consider the S-ramified Iwasawa module which is the Galois group of the maximal abelian pro-p-extension unramified outside S over the cyclotomic ℤ<jats:sub>p</jats:sub>-extension of a number field k. In the case where S does not contain p and k is the rational number field or an imaginary quadratic field, we give the explicit formulae of the ℤ<jats:sub>p</jats:sub>-ranks of the S-ramified Iwasawa modules by using Brumer's p-adic version of Baker's theorem on the linear independence of logarithms of algebraic numbers. </jats:p>

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