Bley, Werner; Cobbe, Alessandro
(2016):
Equivariant epsilon constant conjectures for weakly ramified extensions.
In: Mathematische Zeitschrift, Vol. 283, No. 34: pp. 12171244

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Abstract
We study the local epsilon constant conjecture as formulated by Breuning in Breuning (J London Math Soc 70(2):289306, 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 ArtinLfunctions. 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 localglobal principle we obtain the validity of the global epsilon constant conjecture as formulated in Bley and Burns (Proc Lond Math Soc 87(3):545590, 2003) and of Chinburg's conjecture as stated in Chinburg (Ann Math 121(2):351376, 1985) for certain infinite families F / E of weakly and wildly ramified extensions of number fields.