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Here are some extra references: Amazeen, Étale and Pro-Étale Fundamental Groups; Belmans, Grothendieck Topologies and Étale Cohomology; Bergström--Rydh, Étale Cohomology Spring 2016; Conrad (?), Étale Cohomology; Hajj Chehade, Sheaf Cohomology on Sites and the Leray Spectral Sequence, Chapter 3; Klingler, Étale Cohomology and the Weil Conjectures; Kunkel, ...


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Here's a typical example of what can go wrong in high dimension: Let $\mathcal E$ be an elliptic curve degenerating to a nodal cubic. Let $X = \mathcal E^n$. Then $H^* ( X_{\eta}, \mathbb Q_\ell ) = H^* (E_{\eta}, \mathbb Q_\ell)^{\otimes n}$ where the most interesting piece $H^1( E_{\eta}, \mathbb Q_\ell)$ is a two-dimensional representation with weights $...


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