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 (not necessarily reduced) complex analytic space, and  a coherent analytic sheaf over X. Then,

  for  (resp. ), if  is q-pseudoconvex (resp. q-pseudoconcave). (finiteness)
  for , if  is q-complete. (vanish)

Citations

References

External links

Complex manifolds
Theorems in abstract algebra