Science Fair Project Encyclopedia
Cartan's theorems A and B
In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X. They are significant both as applied to several complex variables, and in the general development of sheaf cohomology.
Theorem A states that F is spanned by its global sections.
Theorem B states that
- Hp(X,F) = {0} for all p > 0.
The analogous properties also hold for coherent sheaves in algebraic geometry, when X is an affine scheme.
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details