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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_2012_76_2_a4,
     author = {L. V. Kuz'min},
     title = {The feeble conjecture on the 2-adic regulator for some 2-extensions},
     journal = {Izvestiya. Mathematics },
     pages = {346--355},
     publisher = {mathdoc},
     volume = {76},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a4/}
}
TY  - JOUR
AU  - L. V. Kuz'min
TI  - The feeble conjecture on the 2-adic regulator for some 2-extensions
JO  - Izvestiya. Mathematics 
PY  - 2012
SP  - 346
EP  - 355
VL  - 76
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a4/
LA  - en
ID  - IM2_2012_76_2_a4
ER  - 
%0 Journal Article
%A L. V. Kuz'min
%T The feeble conjecture on the 2-adic regulator for some 2-extensions
%J Izvestiya. Mathematics 
%D 2012
%P 346-355
%V 76
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a4/
%G en
%F IM2_2012_76_2_a4
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/