\(L\) functions associated to overconvergent \(F\)-isocrystals. II: Unit roots and poles
type: Item
instance of: scholarly article
title: \(L\) functions associated to overconvergent \(F\)-isocrystals. II: Unit roots and poles
zbMATH Open document ID: 0911.14011
published in: Inventiones Mathematicae
publication date: 1997-08-28T00:00:00Z
review text: [For part I of this paper see Math. Ann., 296, No. 3, 557-576 (1993; Zbl 0789.14015).] It is given a construction of the Artin-Schreier exact sequence on the syntomic site of a scheme, not necessarily smooth and proper. Under the last conditions the construction was done by \textit{J. M. Fontaine} and \textit{W. Messing} [in: Current trends in arithmetical algebraic geometry, Proc. Summer Res. Conf., Arcata 1985, Contemp. Math. 67, 179-207 (1987; Zbl 0632.14016)]. N. Katz has conjectured that \(p\)-adic unit roots and poles of the \(L\)-functions associated to a representation of the fundamental group of a variety over \(\mathbb{F}_q\) can be expressed in terms of \(p\)-adic étale cohomologies. The authors prove this conjecture as well as many interesting corollaries.
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14F30
zbMATH DE Number: 1026493
zbMATH Keywords: fundamental group
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: \(p\)-adic étale cohomologies
author: J.-Y. Etesse
author: Bernard Le Stum
reviewed by: A. N. Parshin
MaRDI profile type: Publication
full work available at URL: s002220050112
OpenAlex ID: W2057167992
DOI: 10.1007/S002220050112
description: scientific article; zbMATH DE number 1026493