Lecture 10: Acyclicity of the Ran Space

Since, when $G$ is trivial, $Bun_G(X)$ is  $Spec(k)$, this is the special case of the equivalence of $Ran_G(X)$ to $Bun_G(X)$. I suspect it is everyone's interest to spend more time on Ran space in general. I will also try to fill more historical backgrounds.