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arXiv · 1103.3916

On the Z_p-ranks of tamely ramified Iwasawa modules

Tsuyoshi Itoh·Yasushi Mizusawa·Manabu Ozaki
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Abstract

For a prime number p, we denote by K the cyclotomic Z_p-extension of a number field k. 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 of K unramified outside S. This paper treats the case where S does not contain p and k is the rational number field or an imaginary quadratic field. In this case, we prove the explicit formulae for the free ranks of the S-ramified Iwasawa modules as abelian pro-p groups, by using Brumer's p-adic version of Baker's theorem on the linear independence of logarithms of algebraic numbers.

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Tsuyoshi Itoh, Yasushi Mizusawa, Manabu Ozaki. 2011-03-21. On the Z_p-ranks of tamely ramified Iwasawa modules. https://doi.org/10.1142/s1793042113500395

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