Tsen's theorem

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, and more generally that all the Galois cohomology groups H&thinsp;i(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.