Lemma 59.67.11. Let $C$ be a curve over an algebraically closed field $k$. Then the Brauer group of the function field of $C$ is zero: $\text{Br}(k(C)) = 0$.
Lemma 59.67.11. Let $C$ be a curve over an algebraically closed field $k$. Then the Brauer group of the function field of $C$ is zero: $\text{Br}(k(C)) = 0$.
Proof. This is clear from Tsen's theorem, Theorem 59.67.10 and Theorem 59.67.8. $\square$
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