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Ample filters of invertible sheaves

Dennis S. Keeler
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Abstract

Let $X$ be a scheme, proper over a commutative noetherian ring $A$. We introduce the concept of an ample filter of invertible sheaves on $X$ and generalize the most important equivalent criteria for ampleness of an invertible sheaf. We also prove the Theorem of the Base for $X$ and generalize Serre's Vanishing Theorem. We then generalize results for twisted homogeneous coordinate rings which were previously known only when $X$ was projective over an algebraically closed field. Specifically, we show that the concepts of left and right $\sigma$-ampleness are equivalent and that the associated twisted homogeneous coordinate ring must be noetherian.

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Dennis S. Keeler. 2001-08-09. Ample filters of invertible sheaves. https://doi.org/10.1016/s0021-8693(02)00557-4, 10.1016/j.jalgebra.2018.03.024

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