Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field
Canadian journal of mathematics, Tome 71 (2019) no. 6, pp. 1395-1419
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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 $L$.
Chapdelaine, Hugo; Kučera, Radan. Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field. Canadian journal of mathematics, Tome 71 (2019) no. 6, pp. 1395-1419. doi: 10.4153/CJM-2018-035-9
@article{10_4153_CJM_2018_035_9,
author = {Chapdelaine, Hugo and Ku\v{c}era, Radan},
title = {Annihilators of the {Ideal} {Class} {Group} of a {Cyclic} {Extension} of an {Imaginary} {Quadratic} {Field}},
journal = {Canadian journal of mathematics},
pages = {1395--1419},
year = {2019},
volume = {71},
number = {6},
doi = {10.4153/CJM-2018-035-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-035-9/}
}
TY - JOUR AU - Chapdelaine, Hugo AU - Kučera, Radan TI - Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field JO - Canadian journal of mathematics PY - 2019 SP - 1395 EP - 1419 VL - 71 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-035-9/ DO - 10.4153/CJM-2018-035-9 ID - 10_4153_CJM_2018_035_9 ER -
%0 Journal Article %A Chapdelaine, Hugo %A Kučera, Radan %T Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field %J Canadian journal of mathematics %D 2019 %P 1395-1419 %V 71 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-035-9/ %R 10.4153/CJM-2018-035-9 %F 10_4153_CJM_2018_035_9
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