New answers tagged etale-cohomology
1
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, ...
3
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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