High Quality Content by WIKIPEDIA articles! In mathematics, Tsen's theorem states that a function field K of an algebraic curve over an algebraically closed field is quasi-algebraically closed. This implies that the Brauer group of any such field vanishes, and more generally that all the Galois cohomology groups H?i(K, K*) vanish for i ? 1. This result is used to calculate the etale cohomology groups of an algebraic curve. The theorem was proved by Chiungtze C. Tsen (1933).

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