# Tag Info

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 \$...