The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field and an odd prime dividing the degree assuming that the -part of group is cyclic.
Cet article se propose de démontrer une version analogue de la conjecture de Gras pour un corps abélien et un nombre premier qui divise le degré . On fait l’hypothèse que la -partie du groupe est cyclique.
Keywords: Gras’ conjecture, circular (cyclotomic) units, ideal class group, Euler system, annihilators of the class group
Mot clés : conjecture de Gras, unités cyclotomiques, groupe des classes, systèmes d’Euler, annulateurs du groupe des classes
Greither, Cornelius 1; Kučera, Radan 2
@article{AIF_2014__64_5_2165_0, author = {Greither, Cornelius and Ku\v{c}era, Radan}, title = {Eigenspaces of the ideal class group}, journal = {Annales de l'Institut Fourier}, pages = {2165--2203}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {5}, year = {2014}, doi = {10.5802/aif.2908}, mrnumber = {3330935}, zbl = {06387335}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2908/} }
TY - JOUR AU - Greither, Cornelius AU - Kučera, Radan TI - Eigenspaces of the ideal class group JO - Annales de l'Institut Fourier PY - 2014 SP - 2165 EP - 2203 VL - 64 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2908/ DO - 10.5802/aif.2908 LA - en ID - AIF_2014__64_5_2165_0 ER -
%0 Journal Article %A Greither, Cornelius %A Kučera, Radan %T Eigenspaces of the ideal class group %J Annales de l'Institut Fourier %D 2014 %P 2165-2203 %V 64 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2908/ %R 10.5802/aif.2908 %G en %F AIF_2014__64_5_2165_0
Greither, Cornelius; Kučera, Radan. Eigenspaces of the ideal class group. Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2165-2203. doi : 10.5802/aif.2908. https://aif.centre-mersenne.org/articles/10.5802/aif.2908/
[1] Formules de classes pour les corps abéliens réels, Ann. Inst. Fourier (Grenoble), Volume 51 (2001) no. 4, pp. 903-937 | DOI | Numdam | MR | Zbl
[2] Kolyvagin systems of Stark units, J. Reine Angew. Math., Volume 631 (2009), pp. 85-107 | DOI | MR | Zbl
[3] On -adic -functions and cyclotomic fields. II, Nagoya Math. J., Volume 67 (1977), pp. 139-158 | MR | Zbl
[4] Annihilators for the class group of a cyclic field of prime power degree. II, Canad. J. Math., Volume 58 (2006) no. 3, pp. 580-599 | DOI | MR | Zbl
[5] Linear forms on Sinnott’s module, J. Number Theory, Volume 141 (2014), pp. 324-342 | DOI | MR
[6] Commutative Rings, Polygonal Publishing House, 1994 (Washington, NJ)
[7] Circular units and class groups of abelian fields, Ann. Sci. Math. Québec, Volume 28 (2004) no. 1-2, p. 121-136 (2005) | MR | Zbl
[8] On formulas for the class number of real abelian fields, Izv. Ross. Akad. Nauk Ser. Mat., Volume 60 (1996) no. 4, pp. 43-110 | DOI | MR | Zbl
[9] Class fields of abelian extensions of , Invent. Math., Volume 76 (1984) no. 2, pp. 179-330 | DOI | MR | Zbl
[10] The Main Conjecture, Appendix in S. Lang, Cyclotomic Fields I and II, second ed (Graduate Texts in Mathematics), Volume 121, Springer, New York, 1990
[11] On the Stickelberger ideal and the circular units of an abelian field, Invent. Math., Volume 62 (1980/81) no. 2, pp. 181-234 | DOI | MR | Zbl
[12] On the ideal class groups of real abelian number fields, Ann. of Math. (2), Volume 128 (1988) no. 1, pp. 1-18 | DOI | MR | Zbl
[13] Introduction to cyclotomic fields, Graduate Texts in Mathematics, 83, Springer-Verlag, New York, 1997, pp. xiv+487 | DOI | MR | Zbl
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