Remark 64.29.4. By the proposition and Trivial duality then you get

\[ H^{2-i}_ c(X_{\overline{k}}, \mathcal{F}_\rho ) \times H^ i(X_{\overline{k}}, \mathcal{F}_\rho ^\wedge (1)) \to \mathbf{Q}/\mathbf{Z} \]

a perfect pairing. If $X$ is projective then this is Poincare duality.

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