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Tsen's theorem

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In mathematics, Tsen's theorem states that a function field K of an algebraic curve over an algebraically closed field is quasi-algebraically closed (i.e., C1). This implies that the Brauer group of any such field vanishes,[1] and more generally that all the Galois cohomology groups Hi(K, K*) vanish for i  1. This result is used to calculate the étale cohomology groups of an algebraic curve.

The theorem was published by Chiungtze C. Tsen in 1933.

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