Remark 64.29.2. Thus we conclude that if X is also projective then we have functorially in the representation \rho the identifications
H^0(X_{\overline{k}}, \mathcal{F}_\rho ) = M^{\pi _1(X_{\overline{k}}, \overline\eta )}
and
H_ c^2(X_{\overline{k}}, \mathcal{F}_\rho ) = M_{\pi _1(X_{\overline{k}}, \overline\eta )}(-1)
Of course if X is not projective, then H^0_ c(X_{\overline{k}}, \mathcal{F}_\rho ) = 0.
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