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Search: MSC category 11R37 ( Class field theory )

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1. CMB 2003 (vol 46 pp. 178)

Jaulent, Jean-Fran├žois; Maire, Christian
Sur les invariants d'Iwasawa des tours cyclotomiques
We carry out the computation of the Iwasawa invariants $\rho^T_S$, $\mu^T_S$, $\lambda^T_S$ associated to abelian $T$-ramified over the finite steps $K_n$ of the cyclotomic $\mathbb{Z}_\ell$-extension $K_\infty/K$ of a number field of $\CM$-type. Nous d\'eterminons explicitement les param\'etres d'Iwasawa $\rho^T_S$, $\mu^T_S$, $\lambda^T_S$ des $\ell$-groupes de $S$-classes $T$-infinit\'esimales $\Cl^T_S (K_n)$ attach\'es aux \'etages finis de la $\mathbb{Z}_\ell$-extension cyclotomique $K_\infty/K$ d'un corps de nombres \`a conjugaison complexe.

Categories:11R23, 11R37

2. CMB 2002 (vol 45 pp. 86)

Gerth, Frank
On Cyclic Fields of Odd Prime Degree $p$ with Infinite Hilbert $p$-Class Field Towers
Let $k$ be a cyclic extension of odd prime degree $p$ of the field of rational numbers. If $t$ denotes the number of primes that ramify in $k$, it is known that the Hilbert $p$-class field tower of $k$ is infinite if $t>3+2\sqrt p$. For each $t>2+\sqrt p$, this paper shows that a positive proportion of such fields $k$ have infinite Hilbert $p$-class field towers.

Categories:11R29, 11R37, 11R45

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