Local \(\varepsilon_0\)-characters in torsion rings (Q933168)

Let \(K\) be a complete valued field with a perfect residue field \(k\) of positive characteristic \(p\). Following \textit{P. Deligne} [``Modular functions of one variable II'', Proc. internat. Summer School, Univ. Antwerp 1972, Lect. Notes Math. 349, 501--597 (1973; Zbl 0271.14011)], the author develops a theory of local \(\varepsilon_0\)-constants for representations of the Weil group \(W_K\) of \(K\) over a complete local ring with an algebraically closed residue field of characteristic \(\neq p\). The case of a finite field \(k\) was considered by the author in 2001 (preprint).