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**Bley, Werner and Cobbe, Alessandro (2016): Equivariant epsilon constant conjectures for weakly ramified extensions. In: Mathematische Zeitschrift, Vol. 283, No. 3-4: pp. 1217-1244**

**Full text not available from 'Open Access LMU'.**

## Abstract

We study the local epsilon constant conjecture as formulated by Breuning in Breuning (J London Math Soc 70(2):289-306, 2004). This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected compatibility of the ETNC with the functional equation of Artin-L-functions. Let be unramified. Under some mild technical assumption we prove Breuning's conjecture for weakly ramified abelian extensions N / K with cyclic ramification group. As a consequence of Breuning's local-global principle we obtain the validity of the global epsilon constant conjecture as formulated in Bley and Burns (Proc Lond Math Soc 87(3):545-590, 2003) and of Chinburg's -conjecture as stated in Chinburg (Ann Math 121(2):351-376, 1985) for certain infinite families F / E of weakly and wildly ramified extensions of number fields.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 0025-5874 |

Language: | English |

Item ID: | 47414 |

Date Deposited: | 27. Apr 2018, 08:13 |

Last Modified: | 04. Nov 2020, 13:24 |