Annihilators of the ideal class group of a cyclic extension of
an imaginary quadratic field

J 2019

Annihilators of the ideal class group of a cyclic extension of an imaginary quadratic field

CHAPDELAINE, Hugo and Radan KUČERA

Basic information

Original name

Annihilators of the ideal class group of a cyclic extension of an imaginary quadratic field

Name in Czech

Anihilátory grupy tříd ideálů cyklického rozšíření imaginárního kvadratického tělesa

Authors

CHAPDELAINE, Hugo (124 Canada) and Radan KUČERA (203 Czech Republic, guarantor, belonging to the institution)

Edition

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, CAMBRIDGE, CAMBRIDGE UNIV PRESS, 2019, 0008-414X

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

is not subject to a state or trade secret

References:

Full Text

Impact factor

Impact factor: 0.881

RIV identification code

RIV/00216224:14310/19:00107206

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.4153/CJM-2018-035-9

UT WoS

000496552800005

Keywords (in Czech)

anihilátor; grupa tříd ideálů; eliptická jednotka.

Keywords in English

annihilator; class group; elliptic unit.

Abstract

V originále

The aim of this paper is to study the group of elliptic units of a cyclic extension L of an imaginary quadratic field K such that the degree [L:K] is a power of an odd prime p. We construct an explicit root of the usual top generator of this group and we use it to obtain an annihilation result of the p-Sylow subgroup of the ideal class group of L.

Links

GA15-15785S, research and development project

Name: Grupy tříd ideálů abelovských číselných těles

Investor: Czech Science Foundation

Cite

CHAPDELAINE, Hugo and Radan KUČERA. Annihilators of the ideal class group of a cyclic extension of an imaginary quadratic field. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. CAMBRIDGE: CAMBRIDGE UNIV PRESS, 2019, vol. 71, No 6, p. 1395-1419. ISSN 0008-414X. Available from: https://dx.doi.org/10.4153/CJM-2018-035-9.

@article{1475996,
   author = {Chapdelaine, Hugo and Kučera, Radan},
   article_location = {CAMBRIDGE},
   article_number = {6},
   doi = {http://dx.doi.org/10.4153/CJM-2018-035-9},
   keywords = {annihilator; class group; elliptic unit.},
   language = {eng},
   issn = {0008-414X},
   journal = {CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES},
   title = {Annihilators of the ideal class group of a cyclic extension of an imaginary quadratic field},
   url = {https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/annihilators-of-the-ideal-class-group-of-a-cyclic-extension-of-an-imaginary-quadratic-field/C12CD26099B095A3A08E58AE8E3BE032},
   volume = {71},
   year = {2019}
}

TY  - JOUR
ID  - 1475996
AU  - Chapdelaine, Hugo - Kučera, Radan
PY  - 2019
TI  - Annihilators of the ideal class group of a cyclic extension of an imaginary quadratic field
JF  - CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
VL  - 71
IS  - 6
SP  - 1395-1419
EP  - 1395-1419
PB  - CAMBRIDGE UNIV PRESS
SN  - 0008414X
KW  - annihilator
KW  - class group
KW  - elliptic unit.
UR  - https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/annihilators-of-the-ideal-class-group-of-a-cyclic-extension-of-an-imaginary-quadratic-field/C12CD26099B095A3A08E58AE8E3BE032
L2  - https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/annihilators-of-the-ideal-class-group-of-a-cyclic-extension-of-an-imaginary-quadratic-field/C12CD26099B095A3A08E58AE8E3BE032
N2  - The aim of this paper is to study the group of elliptic units of a cyclic extension L of an imaginary quadratic field K such that the degree [L:K] is a power of an odd prime p. We construct an explicit root of the usual top generator of this group and we use it to obtain an annihilation result of the p-Sylow subgroup of the ideal class group of L.
ER  -

CHAPDELAINE, Hugo and Radan KUČERA. Annihilators of the ideal class group of a cyclic extension of an imaginary quadratic field. \textit{CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES}. CAMBRIDGE: CAMBRIDGE UNIV PRESS, 2019, vol.~71, No~6, p.~1395-1419. ISSN~0008-414X. Available from: https://dx.doi.org/10.4153/CJM-2018-035-9.

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