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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 Hi(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).