Ample filters and Frobenius amplitude

Details Ample filters and Frobenius amplitude Ample filters and Frobenius amplitude

2006-03-16

arxiv.org/abs/math/0603388v2

Mathematics

Algebraic Geometry

15 pages, major improvement in results

Scientific paper

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.

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