Theorem 59.68.5. Let $X$ be a smooth curve over an algebraically closed field. Then

\[ H_{\acute{e}tale}^ q(X, \mathbf{G}_ m) = 0 \ \ \text{ for all } q \geq 2. \]

Theorem 59.68.5. Let $X$ be a smooth curve over an algebraically closed field. Then

\[ H_{\acute{e}tale}^ q(X, \mathbf{G}_ m) = 0 \ \ \text{ for all } q \geq 2. \]

**Proof.**
See discussion above.
$\square$

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