Geodesic
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

Voir la notice de l'article provenant de la source Cambridge University Press

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 $L$.
DOI : 10.4153/CJM-2018-035-9
Mots-clés : annihilator, class group, elliptic unit 
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

[1] Bley, W., Wild Euler systems of elliptic units and the equivariant Tamagawa number conjecture . J. Reine Angew. Math. 577(2004), 117–146. . Google Scholar | DOI

[2] Bley, W., Equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field . Doc. Math. 11(2006), 73–118. Google Scholar

[3] Burns, D., Congruences between derivatives of abelian L-functions at s = 0 . Invent. Math. 169(2007), 451–499. . Google Scholar | DOI

[4] Gras, G., Class field theory. From theory to practice . Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. Google Scholar

[5] Greither, C. and Kučera, R., Annihilators for the class group of a cyclic field of prime power degree . Acta Arith. 112(2004), 177–198. . Google Scholar | DOI

[6] Greither, C. and Kučera, R., Annihilators for the class group of a cyclic field of prime power degree II . Canad. J. Math. 58(2006), 580–599. . Google Scholar | DOI

[7] Greither, C. and Kučera, R., Linear forms on Sinnott’s module . J. Number Theory 141(2014), 324–342. . Google Scholar | DOI

[8] Greither, C. and Kučera, R., Eigenspaces of the ideal class group . Ann. Inst. Fourier (Grenoble) 64(2014), 2165–2203. . Google Scholar | DOI

[9] Greither, C. and Kučera, R., Annihilators for the class group of a cyclic field of prime power degree III . Publ. Math. Debrecen 86(2015), no. 3–4, 401–421. Google Scholar

[10] Ohshita, T., On higher Fitting ideals of Iwasawa modules of ideal class groups over imaginary quadratic fields and Euler systems of elliptic units . Kyoto J. Math. 53(2013), 845–887. . Google Scholar | DOI

[11] Oukhaba, H., Index formulas for ramified elliptic units . Compositio Math. 137(2003), 1–22. . Google Scholar | DOI

[12] Rubin, K., Global units and ideal class groups . Invent. Math. 89(1987), 511–526. . Google Scholar | DOI

[13] Rubin, K., Stark units and Kolyvagin’s “Euler systems” . J. Reine Angew. Math. 425(1992), 141–154. . Google Scholar | DOI

[14] Sinnott, W., On the Stickelberger ideal and the circular units of an abelian field . Invent. Math. 62(1980), 181–234. . Google Scholar | DOI

[15] Thaine, F., On the ideal class groups of real abelian number fields . Ann. of Math. (2) 128(1988), no. 1, 1–18. . Google Scholar | DOI

Cité par Sources :