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arXiv · 1602.07858

The equivariant local $ε$-constant conjecture for unramified twists of $\mathbb{Z}_p(1)$

Werner Bley·Alessandro Cobbe
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Abstract

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 $T=\mathbb{Z}_p(χ^{nr})(1)$ of $\mathbb{Z}_p(1)$. Following ideas of recent work of Izychev and Venjakob we prove that for $T=\mathbb{Z}_p(1)$ a conjecture of Breuning is equivalent to $C_{EP}^{na}(N/K,V)$. As our main result we show 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 $RΓ(N,T)$.

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Werner Bley, Alessandro Cobbe. 2016-02-25. The equivariant local $ε$-constant conjecture for unramified twists of $\mathbb{Z}_p(1)$. https://doi.org/10.4064/aa8567-10-2016

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