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Andreotti–Grauert theorem
Theorem From Wikipedia, the free encyclopedia
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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.
Statement
Let X be a (not necessarily reduced) complex analytic space, and a coherent analytic sheaf over X. Then,
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