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. This implies that the Brauer group of any such field vanishes,[1] and more generally that all the Galois cohomology groups Hi(KK*) vanish for i ≥ 1. This result is used to calculate the étale cohomology groups of an algebraic curve.

The theorem was proved by Zeng Jiongzhi (also rendered as Chiungtze C. Tsen in English) in 1933.

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  1. ^ Lorenz, Falko (2008). Algebra. Volume II: Fields with Structure, Algebras and Advanced Topics. Springer. p. 181. ISBN 978-0-387-72487-4. Zbl 1130.12001.