Article ID Journal Published Year Pages File Type
4587101 Journal of Algebra 2010 15 Pages PDF
Abstract

Let X 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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory