Local constant of \(\text{Ind}^ l_ k 1\)
type: Item
instance of: scholarly article
title: Local constant of \(\text{Ind}^ l_ k 1\)
zbMATH Open document ID: 0870.11073
DOI: 10.1007/BF02566021
author: Takeshi Saito
published in: Commentarii Mathematici Helvetici
publication date: 1997-04-10T00:00:00Z
full work available at URL: https://eudml.org/doc/140381
review text: 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.
Mathematics Subject Classification ID: 11S37
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 852026
zbMATH Keywords: Henniart's formula
zbMATH Keywords: local constant
zbMATH Keywords: local field
zbMATH Keywords: induced representation of the Galois group
zbMATH Keywords: unit representation
reviewed by: Xianke Zhang
MaRDI profile type: Publication
OpenAlex ID: W2022415539
description: scientific article; zbMATH DE number 852026