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arXiv · 2607.09021

Asymptotic Cohomological Functions and Volumes on Proper Schemes

Wenqi Li
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Abstract

We study the behavior of asymptotic cohomological functions on proper schemes over a field. We prove a formula for how asymptotic cohomological functions behave under perturbation by an object in the bounded derived category. Using the same method, we also prove that the volume of a line bundle on any proper scheme over a field always exists as a limit.

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Wenqi Li. 2026-07-10. Asymptotic Cohomological Functions and Volumes on Proper Schemes. https://arxiv.org/abs/2607.09021

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