Geodesic
The feeble conjecture on the 2-adic regulator for some 2-extensions
Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 346-355.

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For an algebraic number field $K$ that is a finite 2-extension of the CM-field $k$ with trivial Iwasawa invariant $\mu_2(k)$, we prove that its cyclotomic $\mathbb Z_\ell$-extension $K_\infty/K$ satisfies the feeble conjecture on the 2-adic regulator [1]. In particular, this conjecture holds for $K_\infty/K$ if $K$ is a 2-extension of a field $k$ that is Abelian over $\mathbb Q$. We also obtain other results in the same direction.
Keywords: cyclotomic $\mathbb Z_\ell$-extension, 2-adic regulator, 2-extension, Iwasawa invariants. 
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L. V. Kuz'min. The feeble conjecture on the 2-adic regulator for some 2-extensions. Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 346-355. http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a4/

[1] L. V. Kuz'min, “Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator”, Math. USSR-Izv., 19:3 (1982), 445–478 | DOI | MR | Zbl

[2] L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. V. Growth of the $\ell$-adic regulator in the cyclotomic $\mathbb{Z}_\ell$-extension of an algebraic number field”, Izv. Math., 73:5 (2009), 959–1021 | DOI | MR | Zbl

[3] L. V. Kuz'min, “Some remarks on the $l$-adic regulator. II”, Math. USSR-Izv., 35:1 (1990), 113–144 | DOI | MR | Zbl

[4] L. V. Kuz'min, “New explicit formulas for the norm residue symbol, and their applications”, Math. USSR-Izv., 37:3 (1991), 555–586 | DOI | MR | Zbl | Zbl

[5] L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. III”, Math. USSR-Izv., 63:6 (1999), 1089–1138 | DOI | MR | Zbl

[6] L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. IV”, Izv. Math., 64:2 (2000), 265–310 | DOI | MR | Zbl