Asymptotic Cohomological Functions and Volumes on Proper Schemes

Wenqi Li

Asymptotic Cohomological Functions and Volumes on Proper Schemes

Algebraic Geometry 2026-07-10 v1

Authors: Wenqi Li

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.

Keywords

asymptotic cohomological functions proper schemes volume line bundle bounded derived category

Cite

@article{arxiv.2607.09021,
  title  = {Asymptotic Cohomological Functions and Volumes on Proper Schemes},
  author = {Wenqi Li},
  journal= {arXiv preprint arXiv:2607.09021},
  year   = {2026}
}

Comments

15 pages. Comments are welcome