Eigenspaces of the ideal class group
[Parties χ-invariantes dans les groupes de classes]
Greither, Cornelius ; Kučera, Radan
Annales de l'Institut Fourier, Tome 64 (2014), p. 2165-2203 / Harvested from Numdam
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Cet article se propose de démontrer une version analogue de la conjecture de Gras pour un corps abélien F et un nombre premier p>2 qui divise le degré [F:ℚ]. On fait l’hypothèse que la p-partie du groupe Gal (F/ℚ) est cyclique.

The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field F and an odd prime p dividing the degree [F:ℚ] assuming that the p-part of Gal (F/ℚ) group is cyclic.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2908
Classification:  11R20,  11R29
Mots clés: conjecture de Gras, unités cyclotomiques, groupe des classes, systèmes d’Euler, annulateurs du groupe des classes 
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     author = {Greither, Cornelius and Ku\v cera, Radan},
     title = {Eigenspaces of the ideal class group},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {2165-2203},
     doi = {10.5802/aif.2908},
     zbl = {06387335},
     mrnumber = {3330935},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_5_2165_0}
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Greither, Cornelius; Kučera, Radan. Eigenspaces of the ideal class group. Annales de l'Institut Fourier, Tome 64 (2014) pp. 2165-2203. doi : 10.5802/aif.2908. http://gdmltest.u-ga.fr/item/AIF_2014__64_5_2165_0/

[1] Belliard, J.-R.; Nguyen Quang Do, T. Formules de classes pour les corps abéliens réels, Ann. Inst. Fourier (Grenoble), Tome 51 (2001) no. 4, pp. 903-937 http://aif.cedram.org/item?id=AIF_2001__51_4_903_0 | Article | Numdam | MR 1849210 | Zbl 1007.11063

[2] Büyükboduk, Kâzim Kolyvagin systems of Stark units, J. Reine Angew. Math., Tome 631 (2009), pp. 85-107 | Article | MR 2542218 | Zbl 1216.11102

[3] Greenberg, Ralph On p-adic L-functions and cyclotomic fields. II, Nagoya Math. J., Tome 67 (1977), pp. 139-158 | MR 444614 | Zbl 0373.12007

[4] Greither, Cornelius; Kučera, Radan Annihilators for the class group of a cyclic field of prime power degree. II, Canad. J. Math., Tome 58 (2006) no. 3, pp. 580-599 | Article | MR 2223457 | Zbl 1155.11054

[5] Greither, Cornelius; Kučera, Radan Linear forms on Sinnott’s module, J. Number Theory, Tome 141 (2014), pp. 324-342 | Article | MR 3195403

[6] Kaplansky, I. Commutative Rings, Polygonal Publishing House (1994) (Washington, NJ)

[7] Kučera, Radan Circular units and class groups of abelian fields, Ann. Sci. Math. Québec, Tome 28 (2004) no. 1-2, p. 121-136 (2005) | MR 2183100 | Zbl 1103.11031

[8] Kuzmin, L. V. On formulas for the class number of real abelian fields, Izv. Ross. Akad. Nauk Ser. Mat., Tome 60 (1996) no. 4, pp. 43-110 | Article | MR 1416925 | Zbl 1007.11065

[9] Mazur, B.; Wiles, A. Class fields of abelian extensions of Q, Invent. Math., Tome 76 (1984) no. 2, pp. 179-330 | Article | MR 742853 | Zbl 0545.12005

[10] Rubin, K. The Main Conjecture, Appendix in S. Lang, Cyclotomic Fields I and II, second ed, Springer, New York (Graduate Texts in Mathematics) Tome 121 (1990)

[11] Sinnott, W. On the Stickelberger ideal and the circular units of an abelian field, Invent. Math., Tome 62 (1980/81) no. 2, pp. 181-234 | Article | MR 595586 | Zbl 0465.12001

[12] Thaine, Francisco On the ideal class groups of real abelian number fields, Ann. of Math. (2), Tome 128 (1988) no. 1, pp. 1-18 | Article | MR 951505 | Zbl 0665.12003

[13] Washington, Lawrence C. Introduction to cyclotomic fields, Springer-Verlag, New York, Graduate Texts in Mathematics, Tome 83 (1997), pp. xiv+487 | Article | MR 1421575 | Zbl 0484.12001