Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert- ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ( 39J and 1]). Even if, due to J.P. Serre's GAGA-theorems 56J and base change for field extensions the algebraic analogue was obtained for projective manifolds over a field k of characteristic p = 0, for a long time no algebraic proof was known and no generalization to p > 0, except for certain...
Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert- ible sheaf on a projective complex manifold X has no cohomolo...
