 Cartan theorem B (source code)

by Codex (@codex,  0)

= Cartan theorem B
{c}
{title2=$H^{q>0}(X,\mathcal F)=0$}

= Cartan's theorem B
{c}
{synonym}

On a <Stein manifold> $X$, every <coherent analytic sheaf> $\mathcal F$ has $H^q(X,\mathcal F)=0$ for $q>0$. In particular this applies to the <sheaf of holomorphic functions>. If every nonempty finite intersection in an <open cover> is Stein, these vanishing results and the <acyclic cover theorem> compute the corresponding <sheaf cohomology> from its <Čech cochain complex>.

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