  We study the local epsilon constant conjecture as formulated by Breuning.
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 K / Q_p 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 by Bley and Burns and of Chinburg's
Omega(2)-conjecture for certain infinite families F / E of weakly and wildly
ramified extensions of number fields.
