Andreotti–Grauert theorem

In mathematics, the Andreotti–Grauert theorem, introduced by Andreotti and Grauert (1962), gives conditions for cohomology groups of coherent sheaves over complex manifolds to vanish or to be finite-dimensional.

Let X be a (not necessarily reduced) complex analytic space, and

a coherent analytic sheaf over X.

(2001) [1994], "Finiteness theorems", Encyclopedia of Mathematics, EMS Press

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