Local constant of \(\text{Ind}^ l_ k 1\)
The author shows that Henniart's formula for the local constant \(\epsilon(\text{Ind} 1) \) of \(L/K\) is a consequence of results of Serre and Deligne (see \textit{G. Henniart} [Invent. Math. 78, 117-126 (1984; Zbl 0557.12011)], \textit{J.-P. Serre} [Comment. Math. Helv. 59, 651-676 (1984; Zbl 0565.12014)] and \textit{P. Deligne} [Invent. Math. 35, 299-316 (1976; Zbl 0337.12012)]), where \(K\) is a local field (i.e. a complete discrete valuation field with finite residue field), \(L\) a separable extension of odd degree over \(K\), Ind \(1\) is the induced representation of the Galois group \(G_K\) over \(K\) from the unit representation \(1\) of \(G_L\), and \(\epsilon(\text{Ind} 1)\) is the related local constant [see \textit{P. Deligne}, Lect. Notes Math. 349, 501-597 (1973; Zbl 0271.14011)]. He also computes the local constant for an extension \(L/K\) of even degree.
induced representation of the Galois group
scientific article; zbMATH DE number 852026