Tsen's theorem

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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 etale cohomology groups of an algebraic curve.

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

[edit] 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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