Tsen's theorem

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 etale cohomology groups of an algebraic curve. The theorem was proved by Chiungtze C. Tsen (1933).

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, [http://links.jstor.org/sici?sici=0003-486X%28195203%292%3A55%3A2%3C373%3AOQAC%3E2.0.CO%3B2-W "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


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Chiungtze Tsen — Chiungtze Chiung Tsen, englische Transkription auch Zeng Jiongzhi, (* 2. April 1898 in Hsienkien (Xinjian) bei Nanchang; † November 1940 in Xichang) war ein chinesischer Mathematiker, der sich mit Algebra beschäftigte. Tsen, der Sohn armer… …   Deutsch Wikipedia

  • Emmy Noether — Portrait de Emmy Noether avant 1910. Naissance 23 mars 1882 Erlangen (Bavière, Allemagne) Décès 14 avril  …   Wikipédia en Français

  • Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   Wikipedia

  • Quasi-algebraically closed field — In mathematics, a field F is called quasi algebraically closed (or C1) if for every non constant homogeneous polynomial P over F has a non trivial zero provided the number of its variables is more than its degree. In other words, if P is a non… …   Wikipedia

  • Zeng Jiongzhi — (Chinese: 曾炯之; pinyin: Zēng Jiǒngzhī; Wade–Giles: Tseng Chiung chih, April 2, 1898–1940), also known as Chiungtze C. Tsen, was a Chinese mathematician born in Nanchang, Jiangxi, who proved Tsen s theorem. He was one of Emmy Noether s students at… …   Wikipedia

  • List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

  • List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

  • 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… …   Wikipedia

  • Brauer group — In mathematics, the Brauer group arose out of an attempt to classify division algebras over a given field K . It is an abelian group with elements isomorphism classes of division algebras over K , such that the center is exactly K . The group is… …   Wikipedia

  • Noether — Emmy Noether Emmy Noether Amalie Emmy Noether (23 mars 1882 14 avril 1935) était une mathématicienne allemande connue pour ses contributions révolutionnaires en algèbre abstraite et physique théorique. Décrite par Albert Einstein et d autres… …   Wikipédia en Français

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”