Annihilators of minus class groups of imaginary abelian fields

Cornelius Greither[1]; Radan Kučera[2]

  • [1] Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik und Mathematik 85577 Neubiberg (Germany)
  • [2] Masarykova univerzita Přírodovědecká fakulta Janáčkovo nám. 2a 602 00 Brno (Czech Republic)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 5, page 1623-1653
  • ISSN: 0373-0956

Abstract

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For certain imaginary abelian fields we find annihilators of the minus part of the class group outside the Stickelberger ideal. Depending on the exact situation, we use different techniques to do this. Our theoretical results are complemented by numerical calculations concerning borderline cases.

How to cite

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Greither, Cornelius, and Kučera, Radan. "Annihilators of minus class groups of imaginary abelian fields." Annales de l’institut Fourier 57.5 (2007): 1623-1653. <http://eudml.org/doc/10273>.

@article{Greither2007,
abstract = {For certain imaginary abelian fields we find annihilators of the minus part of the class group outside the Stickelberger ideal. Depending on the exact situation, we use different techniques to do this. Our theoretical results are complemented by numerical calculations concerning borderline cases.},
affiliation = {Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik und Mathematik 85577 Neubiberg (Germany); Masarykova univerzita Přírodovědecká fakulta Janáčkovo nám. 2a 602 00 Brno (Czech Republic)},
author = {Greither, Cornelius, Kučera, Radan},
journal = {Annales de l’institut Fourier},
keywords = {Imaginary abelian number fields; minus part of the ideal class group; annihilators; Stickelberger ideal; Fitting ideals},
language = {eng},
number = {5},
pages = {1623-1653},
publisher = {Association des Annales de l’institut Fourier},
title = {Annihilators of minus class groups of imaginary abelian fields},
url = {http://eudml.org/doc/10273},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Greither, Cornelius
AU - Kučera, Radan
TI - Annihilators of minus class groups of imaginary abelian fields
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 5
SP - 1623
EP - 1653
AB - For certain imaginary abelian fields we find annihilators of the minus part of the class group outside the Stickelberger ideal. Depending on the exact situation, we use different techniques to do this. Our theoretical results are complemented by numerical calculations concerning borderline cases.
LA - eng
KW - Imaginary abelian number fields; minus part of the ideal class group; annihilators; Stickelberger ideal; Fitting ideals
UR - http://eudml.org/doc/10273
ER -

References

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  1. P. Cornacchia, C. Greither, Fitting ideals of class groups of real fields with prime power conductor, J. Number Theory 73 (1998), 459-471 Zbl0926.11085MR1658000
  2. H. Darmon, Thaine’s method for circular units and a conjecture of Gross, Canad. J. Math. 47 (1995), 302-317 Zbl0844.11071
  3. C. Greither, Über relativ-invariante Kreiseinheiten und Stickelberger-Elemente, Manuscripta Math. 80 (1993), 27-43 Zbl0801.11044MR1226595
  4. Cornelius Greither, Some cases of Brumer’s conjecture for abelian CM extensions of totally real fields, Math. Z. 233 (2000), 515-534 Zbl0965.11047
  5. 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
  6. A. Hayward, A class number formula for higher derivatives of abelian L -functions, Compos. Math. 140 (2004), 99-129 Zbl1060.11075MR1984423
  7. I. Kaplansky, Commutative rings, (1994), Polygonal Publishing House, Washington, NJ Zbl0814.16032
  8. M. Kurihara, Iwasawa theory and Fitting ideals, J. Reine Angew. Math. 561 (2003), 39-86 Zbl1056.11063MR1998607
  9. Serge Lang, Cyclotomic fields I and II, 121 (1990), Springer-Verlag, New York Zbl0395.12005MR1029028
  10. W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980/81), 181-234 Zbl0465.12001MR595586
  11. Lawrence C. Washington, Introduction to cyclotomic fields, 83 (1982), Springer-Verlag, New York Zbl0484.12001MR718674

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