Decomposition theorem for good moduli morphisms

Abstract

In this short note, we will explain that the good moduli space morphisms behave as if they are proper when we consider sheaf operations, though they are not separated. For example, the decomposition theorem and the base change theorem hold for these morphisms, which have applications to the cohomological study of moduli spaces.

arXiv comment6 pages. v2: Corrected the statement of Theorem 5.7