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

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane ...

over an algebraically closed field is quasi-algebraically closed (i.e., C₁). This implies that the

Brauer group Brauer or Bräuer is a surname of German origin, meaning "brewer". Notable people with the name include:- * Alfred Brauer (1894–1985), German-American mathematician, brother of Richard * Andreas Brauer (born 1973), German film producer * Arik ...

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

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. A Galois group ''G'' associated to a field extension ''L''/''K'' acts in a nat ...

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

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 conject ...

groups of an algebraic curve. The theorem was published by Chiungtze C. Tsen in 1933.

References

* * * * Theorems in algebraic geometry {{algebraic-geometry-stub

See also

References