Kato's local epsilon conjecture: \(l\neq p\) case
type: Item
instance of: scholarly article
zbMATH Open document ID: 1356.11079
author: Mahesh Kakde
publication date: 2014-08-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1301.2333
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11S40
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 6327938
zbMATH Keywords: Kato's local \(\varepsilon\)-conjecture
zbMATH Keywords: Iwasawa algebras
zbMATH Keywords: \(p\)-adic Lie groups
zbMATH Keywords: \(L\)-functions
Wikidata QID: Q123260670
MaRDI profile type: Publication
OpenAlex ID: W2593212334
arXiv ID: 1301.2333
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DOI: 10.1112/JLMS/JDU022
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title: Kato's local epsilon conjecture: \(l\neq p\) case
published in: Journal of the London Mathematical Society. Second Series
review text: 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 II'', Preprint (unpublished)] (for commutative Iwasawa algebras) and \textit{T. Fukaya} and \textit{K. Kato} [in: Proceedings of the St. Petersburg Mathematical Society.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).
reviewed by: Denis Ibadula
description: scientific article; zbMATH DE number 6327938