Cartan’s theorem B
On a Stein manifold $\Sigma$ and for $A$ an analytic coherent sheaf on $\Sigma$ then all the positive-degree abelian sheaf cohomology groups of $\Sigma$ with coefficients in $A$ vanish:
This is recalled for instance as (Forstnerič 11, theorem 2.4.1)
Also all positive-degree Dolbeault cohomology groups vanish:
This is recalled for instance in (Forstnerič 11, theorem 2.4.6, Gunning-Rossi).
Named after Henri Cartan.
Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall Inc., Englewood Cliffs, N.J., (1965)
Franc Forstnerič, Stein manifolds and holomorphic mappings – The homotopy principle in complex analysis, Springer 2011
Last revised on May 28, 2014 at 06:29:00. See the history of this page for a list of all contributions to it.