On non-abelian Stark-type conjectures

Andreas Nickel[1]

  • [1] Universität Regensburg Fakultät für Mathematik Universitätsstr. 31 93053 Regensburg, Germany

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2577-2608
  • ISSN: 0373-0956

Abstract

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We introduce non-abelian generalizations of Brumer’s conjecture, the Brumer-Stark conjecture and the strong Brumer-Stark property attached to a Galois CM-extension of number fields. Moreover, we discuss how they are related to the equivariant Tamagawa number conjecture, the strong Stark conjecture and a non-abelian generalization of Rubin’s conjecture due to D. Burns.

How to cite

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Nickel, Andreas. "On non-abelian Stark-type conjectures." Annales de l’institut Fourier 61.6 (2011): 2577-2608. <http://eudml.org/doc/219691>.

@article{Nickel2011,
abstract = {We introduce non-abelian generalizations of Brumer’s conjecture, the Brumer-Stark conjecture and the strong Brumer-Stark property attached to a Galois CM-extension of number fields. Moreover, we discuss how they are related to the equivariant Tamagawa number conjecture, the strong Stark conjecture and a non-abelian generalization of Rubin’s conjecture due to D. Burns.},
affiliation = {Universität Regensburg Fakultät für Mathematik Universitätsstr. 31 93053 Regensburg, Germany},
author = {Nickel, Andreas},
journal = {Annales de l’institut Fourier},
keywords = {Stark conjectures; $L$-values; class groups; Brumer conjecture; Brumer-Stark; annihilators; Fitting ideals; noncommutative rings; maximal orders; reduced norms},
language = {eng},
number = {6},
pages = {2577-2608},
publisher = {Association des Annales de l’institut Fourier},
title = {On non-abelian Stark-type conjectures},
url = {http://eudml.org/doc/219691},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Nickel, Andreas
TI - On non-abelian Stark-type conjectures
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2577
EP - 2608
AB - We introduce non-abelian generalizations of Brumer’s conjecture, the Brumer-Stark conjecture and the strong Brumer-Stark property attached to a Galois CM-extension of number fields. Moreover, we discuss how they are related to the equivariant Tamagawa number conjecture, the strong Stark conjecture and a non-abelian generalization of Rubin’s conjecture due to D. Burns.
LA - eng
KW - Stark conjectures; $L$-values; class groups; Brumer conjecture; Brumer-Stark; annihilators; Fitting ideals; noncommutative rings; maximal orders; reduced norms
UR - http://eudml.org/doc/219691
ER -

References

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