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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„The equivariant local epsilon constant conjecture for unramified twists of Zp(1)“
Dr. Alessandro Cobbe, Universität der Bundeswehr München

We study the equivariant local epsilon constant conjecture, denoted by $C_{EP}^{na}(N/K, V)$, as formulated in various forms by Kato, Benois and Berger, Fukaya and Kato and others, for certain $1$-dimensional twists $T = \mathbb{Z}_p(\chi^{\mathrm{nr}})(1)$ of $\mathbb{Z}_p(1)$. Following ideas of recent work of Izychev and Venjakob it is possible to prove that for $T = \mathbb{Z}_p(1)$ a conjecture of Breuning is equivalent to $C_{EP}^{na}(N/K,V)$. Our main result is the validity of $C_{EP}^{na}(N/K, V)$ for certain wildly and weakly ramified abelian extensions $N/K$. A crucial step in the proof is the construction of an explicit representative of $R\Gamma(N, T)$. This is a joint work with Werner Bley.

Freitag, den 10. Juni 2016 um 13:30 Uhr, in INF205, SR C Freitag, den 10. Juni 2016 at 13:30, in INF205, SR C

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Otmar Venjakob