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

Kurihara, Masato. "On the ideal class groups of the maximal real subfields of number fields with all roots of unity." Journal of the European Mathematical Society 001.1 (1999): 35-49. <http://eudml.org/doc/277481>.

@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 -