Vol. 4, No. 1, 2022

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Constructibilité générique et uniformité en $\ell$

Luc Illusie

Vol. 4 (2022), No. 1, 159–181
DOI: 10.2140/tunis.2022.4.159
Abstract

Cet article, écrit en 2010, présente divers résultats de constructibilité générique et d’indépendance de pour des images directes en cohomologie étale, dans le cas de coefficients constants n ou . On donne une application à un résultat de Serre d’indépendance de représentations -adiques (Comment. Math. Helv. 88 (2013), 541–554). On formule quelques questions relatives au cas des coefficients non constants.

Je n’ai pas modifié la rédaction initiale. Je me suis borné à ajouter des notes de bas de page pour actualiser certains points, et mettre à jour les références.

The present paper, written in 2010, presents various results on generic constructibility and independence of for direct images in étale cohomology in the case of constant coefficients n or . We give an application to a result of Serre of independence of -adic representations (Comment. Math. Helv. 88 (2013), 541–554). We formulate questions in the case of nonconstant coefficients.

I have not modified the initial redaction. I limited myself to refreshing references and adding footnotes for updating certain points.

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Keywords
cohomologie étale, cohomologie $\ell$-adique, faisceau constructible, représentation $\ell$-adique, altération, corps de nombres, corps de fonctions, cohomologie cristalline, schéma simplicial, hyperrecouvrement, descente cohomologique, log schéma, théorie de Hodge $p$-adique
Mathematical Subject Classification
Primary: 11F80, 14F08, 14F20, 14F30, 14G25
Milestones
Received: 9 May 2021
Revised: 9 August 2021
Accepted: 6 September 2021
Published: 30 March 2022
Authors
Luc Illusie
Laboratoire de Mathématiques d’Orsay, CNRS
Université Paris-Saclay
Orsay
France