Tsen\'s theorem - Citizendia

In mathematics, Tsen's theorem states that a function field K of an algebraic curve over an algebraically closed field is quasi-algebraically closed. In Algebraic geometry, an algebraic curve is an Algebraic variety of dimension one In Mathematics, a field F is called quasi-algebraically closed (or C1) if for every non-constant Homogeneous polynomial 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. In Mathematics, the Brauer group arose out of an attempt to classify Division algebras over a given field K. In Mathematics, Galois cohomology is the study of the Group cohomology of Galois modules that is the application of Homological algebra to This result is used to calculate the etale cohomology groups of an algebraic curve. 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

The theorem was proved by Chiungtze C. Tsen (1933). Zeng Jiongzhi ( April 2 1898 – 1940) also known as Chiungtze C

References

Ding, Shisun; Kang, Ming-Chang; Tan, Eng-Tjioe Chiungtze C. Tsen (1898-1940) and Tsen's theorems. Rocky Mountain J. Math. 29 (1999), no. 4, 1237-1269.
Serge Lang, On Quasi Algebraic Closure The Annals of Mathematics 2nd Ser. , Vol. 55, No. 2 (Mar. , 1952), pp. 373-390
J.-P. Serre, Galois cohomology, ISBN 3540421920
C. Tsen, Divisionsalgebren über Funkionenkörper, Nachr. Ge. Wiss. Gottingen (1933) p. 335

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