Eigenspaces of the ideal class group

Cornelius Greither[1]; Radan Kučera[2]

  • [1] Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik, Mathematik und OR 85577 Neubiberg (Germany)
  • [2] Masaryk University Faculty of Science 611 37 Brno (Czech Republic)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 5, page 2165-2203
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Greither, Cornelius, and Kučera, Radan. "Eigenspaces of the ideal class group." Annales de l’institut Fourier 64.5 (2014): 2165-2203. <http://eudml.org/doc/275624>.

@article{Greither2014,
abstract = {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 $[F:\{\mathbb\{Q\}\}]$ assuming that the $p$-part of $\{\rm Gal\}(F/\{\mathbb\{Q\}\})$ group is cyclic.},
affiliation = {Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik, Mathematik und OR 85577 Neubiberg (Germany); Masaryk University Faculty of Science 611 37 Brno (Czech Republic)},
author = {Greither, Cornelius, Kučera, Radan},
journal = {Annales de l’institut Fourier},
keywords = {Gras’ conjecture; circular (cyclotomic) units; ideal class group; Euler system; annihilators of the class group; Gras' conjecture; Sinnott group of circular units; eigenspaces of the ideal class group; Euler systems},
language = {eng},
number = {5},
pages = {2165-2203},
publisher = {Association des Annales de l’institut Fourier},
title = {Eigenspaces of the ideal class group},
url = {http://eudml.org/doc/275624},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Greither, Cornelius
AU - Kučera, Radan
TI - Eigenspaces of the ideal class group
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 5
SP - 2165
EP - 2203
AB - 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 $[F:{\mathbb{Q}}]$ assuming that the $p$-part of ${\rm Gal}(F/{\mathbb{Q}})$ group is cyclic.
LA - eng
KW - Gras’ conjecture; circular (cyclotomic) units; ideal class group; Euler system; annihilators of the class group; Gras' conjecture; Sinnott group of circular units; eigenspaces of the ideal class group; Euler systems
UR - http://eudml.org/doc/275624
ER -

References

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  1. J.-R. Belliard, T. Nguyen Quang Do, Formules de classes pour les corps abéliens réels, Ann. Inst. Fourier (Grenoble) 51 (2001), 903-937 Zbl1007.11063MR1849210
  2. Kâzim Büyükboduk, Kolyvagin systems of Stark units, J. Reine Angew. Math. 631 (2009), 85-107 Zbl1216.11102MR2542218
  3. Ralph Greenberg, On p -adic L -functions and cyclotomic fields. II, Nagoya Math. J. 67 (1977), 139-158 Zbl0373.12007MR444614
  4. Cornelius Greither, Radan Kučera, Annihilators for the class group of a cyclic field of prime power degree. II, Canad. J. Math. 58 (2006), 580-599 Zbl1155.11054MR2223457
  5. Cornelius Greither, Radan Kučera, Linear forms on Sinnott’s module, J. Number Theory 141 (2014), 324-342 Zbl1309.11079MR3195403
  6. I. Kaplansky, Commutative Rings, Polygonal Publishing House (1994) 
  7. Radan Kučera, Circular units and class groups of abelian fields, Ann. Sci. Math. Québec 28 (2004), 121-136 (2005) Zbl1103.11031MR2183100
  8. L. V. Kuzmin, On formulas for the class number of real abelian fields, Izv. Ross. Akad. Nauk Ser. Mat. 60 (1996), 43-110 Zbl1007.11065MR1416925
  9. B. Mazur, A. Wiles, Class fields of abelian extensions of Q , Invent. Math. 76 (1984), 179-330 Zbl0545.12005MR742853
  10. K. Rubin, The Main Conjecture, Appendix in S. Lang, Cyclotomic Fields I and II, second ed 121 (1990), Springer, New York 
  11. W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980/81), 181-234 Zbl0465.12001MR595586
  12. Francisco Thaine, On the ideal class groups of real abelian number fields, Ann. of Math. (2) 128 (1988), 1-18 Zbl0665.12003MR951505
  13. Lawrence C. Washington, Introduction to cyclotomic fields, 83 (1997), Springer-Verlag, New York Zbl0484.12001MR1421575

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