Kato's local epsilon conjecture: \(l\neq p\) case (Q2874660)

In the present paper, the author prove, up to uniqueness, Kato's local \(\varepsilon\)-conjecture in the \(l\neq p\) case. More precisely, let \(l\) and \(p\) be two distinct primes. Let \(K\) be a local field of characteristic \(0\) and residue characteristic \(l\). Then there exists, up to uniqueness, local \(\varepsilon_0\)-constants for representations of \(\operatorname{Gal}(\bar{K}/K)\) over Iwasawa algebras of \(p\)-adic Lie groups.NEWLINENEWLINENEWLINENEWLINEThe existence of these \(\varepsilon_0\)-constants was conjectured by \textit{K. Kato} [``Lectures on the approach to Iwasawa theory for Hasse Weil \(L\)-functions via \(B_d R\). II'', Preprint (unpublished)] (for commutative Iwasawa algebras) and \textit{T. Fukaya} and \textit{K. Kato} [in: Proceedings of the St. Petersburg Mathematical Society. Vol. XII. Transl. from the Russian. Providence, RI: American Mathematical Society (AMS). 1--85 (2006; Zbl 1238.11105)] (in general).