Asymptotic Cohomological Functions and Volumes on Proper Schemes

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.

15 pages. Comments are welcome