Let $X$ be a reasonable topological space. If $\mathcal{F}$ is a sheaf of abelian groups then Cech cohomology gives us a method to compute the cohomology groups $H^p(X, \mathcal{F})$ – the main input being the sections $\mathcal{F}(U)$ for various open sets $U \subset X$.
I would like to have a similar procedure to compute hypercohomology of a finite complex $C^\cdot$ of abelian sheaves on $X$ (or coherent sheaves on a scheme). Is this possible, and is there a reference you can recommend? I couldn't find this in the Stacks project, which incidently explains how to compute cohomology of a complex (not hypercohomology) via a Cech argument.
Best Answer
There is a nice treatment of it in chapter 1 of Brylisnki's Loop Spaces, Characteristic Classes and Geometric Quantization. In the Stacks projects, look for section 19.19.