The Stacks project

103.1 Introduction

In this chapter we write about cohomology of algebraic stacks. This means in particular cohomology of quasi-coherent sheaves, i.e., we prove analogues of the results in the chapters entitled “Cohomology of Schemes” and “Cohomology of Algebraic Spaces”. The results in this chapter are different from those in [LM-B] mainly because we consistently use the “big sites”. Before reading this chapter please take a quick look at the chapter “Sheaves on Algebraic Stacks” in order to become familiar with the terminology introduced there, see Sheaves on Stacks, Section 96.1.