Andreotti–Grauert theorem

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

Statement

Let be a complex analytic space, and a coherent analytic sheaf over X. Then,

for, if is q-pseudoconvex.
for, if is q-complete.