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Third Italian Number Theory Meeting

Equivariant epsilon constant conjectures for weakly ramified extensions

speaker: Alessandro Cobbe (Universit√§t der Bundeswehr M√ľnchen)

abstract: We study the local epsilon constant conjecture as formulated by M. 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 $K\mathbb Qp$ be unramified. Under some mild technical assumption we prove Breuning's conjecture for weakly ramified abelian extensions $NK$ 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 $FE$ of weakly and wildly ramified extensions of number fields. This is a joint work with Werner Bley.

Mon 21 Sep, 15:30 - 15:55, Aula Contini
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