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., C<sub>1</sub>). This implies that the Brauer group of any such field vanishes, and more generally that all the Galois cohomology groups H<sup> i</sup>(K, K<sup>*</sup>) vanish for i âÂÂ¥ 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.