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. This implies that the Brauer group of any such field vanishes, and more generally that all the Galois cohomology groups H i(K, K*) vanish for i ≥ 1. This result is used to calculate the étale cohomology groups of an algebraic curve.
The theorem was proved by Chiungtze C. Tsen (1933).
References
- Ding, Shisun; Kang, Ming-Chang; Tan, Eng-Tjioe (1999), "Chiungtze C. Tsen (1898--1940) and Tsen's theorems", The Rocky Mountain Journal of Mathematics, 29 (4): 1237–1269, doi:10.1216/rmjm/1181070405, ISSN 0035-7596, MR1743370
- 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. Göttingen (1933) p. 335
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