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Tsen's theorem

From Wikipedia, the free encyclopedia

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., C1). This implies that the Brauer group of any such field vanishes,[1] and more generally that all the Galois cohomology groups Hi(KK*) vanish for i ≥ 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.

See also

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References

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  1. ^ Lorenz, Falko (2008). Algebra. Volume II: Fields with Structure, Algebras and Advanced Topics. Springer. p. 181. ISBN 978-0-387-72487-4. Zbl 1130.12001.