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

Journal of the European Mathematical Society (1999)

- Volume: 001, Issue: 1, page 35-49
- ISSN: 1435-9855

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topKurihara, 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 -

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