Constructibilité générique et uniformité en ℓ

摘要

The present paper, written in 2010, presents various results on generic constructibility and independence of ℓ for direct images in étale cohomology in the case of constant coefficients ℤ∕ℓnℤ or ℤℓ. We give an application to a result of Serre of independence of ℓ-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.