Ample filters and Frobenius amplitude
Algebraic Geometry
2018-05-11 v4
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.
Cite
@article{arxiv.math/0603388,
title = {Ample filters and Frobenius amplitude},
author = {Dennis S. Keeler},
journal= {arXiv preprint arXiv:math/0603388},
year = {2018}
}
Comments
15 pages, major improvement in results, typo fixed in Equation 2.5, warning footnote added to Lemma 2.2