Let $X$ be a Kähler manifold. [This answer on MO](https://mathoverflow.net/questions/57830/picard-group-fundamental-group-and-deformation/57839#57839) quotes the exact sequence
$$0 \to H^1(X, \mathbb{Z}) \to H^{0,1}(X) \to \operatorname{Pic}^0(X) \to 0$$
where $H^{0,1}(X) = H^1(X, \mathscr{O}\_X)$ (I think).

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> **Question:** Is there an analogous exact sequence when $X$ is a smooth projective variety over an arbitrary field? If so, where can I find a derivation of this result?
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