2006/03/31 by Dennis S. Keeler · 1 citation
Mathematics · #math.AG #msc:14F05 #msc:14F17
paper · pdf · doi:10.1016/j.jalgebra.2010.02.028
published as J. Algebra 323 (2010), no. 10, 3039-3053 · 15 pages, major improvement in results, typo fixed in Equation 2.5, warning footnote added to Lemma 2.2
arxiv created 2018/05/09 · arxiv updated 2018/05/11
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.