In mathematics, Tsen's theorem states that a function field K of an algebraic curve

Algebraic curve

In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...

 over an algebraically closed field is quasi-algebraically closed. This implies that the Brauer group

Brauer group

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras of finite rank over K and addition is induced by the tensor product of algebras. It arose out of attempts to classify division algebras over a field and is...

 of any such field vanishes, and more generally that all the Galois cohomology

Galois cohomology

In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups...

 groups Hⁱ(K, K^*) vanish for i ≥ 1. This result is used to calculate the étale cohomology

Étale cohomology

In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures...

 groups of an algebraic curve.

The theorem was proved by Chiungtze C. Tsen (1933).