For any prime number $p$, we study local triviality of the ideal class group of
the ${\boldsymbol Z}_p$-extension over the rational field. We improve a known
general result in such study by modifying the proof of the result, and pursue
known effective arguments on the above triviality with the help of a computer.
Some explicit consequences of our investigations are then provided in the case
$p\leq7$.
Publié le : 2009-05-15
Classification:
Ideal class group,
boldsymbol Z}_p$-extension,
11R29,
11R18,
11R20,
11R23
@article{1264084499,
author = {Horie, Kuniaki and Horie, Mitsuko},
title = {The ideal class group of the $\boldsymbol{Z}\_p$-extension over the rationals},
journal = {Tohoku Math. J. (2)},
volume = {61},
number = {1},
year = {2009},
pages = { 551-570},
language = {en},
url = {http://dml.mathdoc.fr/item/1264084499}
}
Horie, Kuniaki; Horie, Mitsuko. The ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp. 551-570. http://gdmltest.u-ga.fr/item/1264084499/