\(L\)-functions associated to overconvergent \(F\)-isocrystals
type: Item
instance of: scholarly article
title: \(L\)-functions associated to overconvergent \(F\)-isocrystals
zbMATH Open document ID: 0789.14015
DOI: 10.1007/BF01445120
author: J.-Y. Etesse
author: Bernard Le Stum
published in: Mathematische Annalen
publication date: 1994-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/165100
review text: We prove the formulas that give the cohomological expressions of the \(L\)- function attached to an overconvergent \(F\)-isocristal. We deduce that such an \(L\)-function is always meromorphic. This applies in particular to the \(L\)-functions that arise in the study of classical exponential sums. We also show that Frobenius is always bijective on rigid cohomology with or without support and that the trace of Frobenius on the highest rigid cohomology space with compact support of a scheme of pure dimension \(n\) is multiplication by \(q^ n\).
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 11G40
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 11L03
zbMATH DE Number: 537267
zbMATH Keywords: \(L\)-function
zbMATH Keywords: overconvergent \(F\)-isocristal
zbMATH Keywords: Frobenius on rigid cohomology
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537267