Ample filters and Frobenius amplitude
arXiv:math/0603388 · doi:10.1016/j.jalgebra.2010.02.028
Abstract
Let be a projective scheme over a field. We show that the vanishing cohomology of any sequence of coherent sheaves is closely related to vanishing under pullbacks by the Frobenius morphism. We also compare various definitions of ample locally free sheaf and show that the vanishing given by the Frobenius morphism is, in a certain sense, the strongest possible. Our work can be viewed as various generalizations of the Serre Vanishing Theorem.
15 pages, major improvement in results, typo fixed in Equation 2.5, warning footnote added to Lemma 2.2