On the ideal class groups of the maximal real subfields of number fields with all roots of unity

@article{Kurihara1999,
abstract = {In this paper, for a totally real number field $k$ we show the ideal class group of $k(\cup _\{n>0\}\mu _n)^+$ is trivial. We also study the $p$-component of the ideal class group of the cyclotomic $\mathbf \{Z\}_p$-extension.},
author = {Kurihara, Masato},
journal = {Journal of the European Mathematical Society},
keywords = {ideal class group; $p$-component; cyclotomic $\mathbf \{Z\}_p$-extension; Iwasawa theory; class groups; maximal real subfields; Galois cohomology; existence of infinitely many real abelian extensions; Greenberg's conjecture},
language = {eng},
number = {1},
pages = {35-49},
publisher = {European Mathematical Society Publishing House},
title = {On the ideal class groups of the maximal real subfields of number fields with all roots of unity},
url = {http://eudml.org/doc/277481},
volume = {001},
year = {1999},
}

TY - JOUR
AU - Kurihara, Masato
TI - On the ideal class groups of the maximal real subfields of number fields with all roots of unity
JO - Journal of the European Mathematical Society
PY - 1999
PB - European Mathematical Society Publishing House
VL - 001
IS - 1
SP - 35
EP - 49
AB - In this paper, for a totally real number field $k$ we show the ideal class group of $k(\cup _{n>0}\mu _n)^+$ is trivial. We also study the $p$-component of the ideal class group of the cyclotomic $\mathbf {Z}_p$-extension.
LA - eng
KW - ideal class group; $p$-component; cyclotomic $\mathbf {Z}_p$-extension; Iwasawa theory; class groups; maximal real subfields; Galois cohomology; existence of infinitely many real abelian extensions; Greenberg's conjecture
UR - http://eudml.org/doc/277481
ER -