I am watching Scholze's masterclass on Condensed Mathematics and I don't understand or can find any references on something he said.
You have a resolution
$$ \dots \to \mathbb{Z}[\mathbb{R}^2] \to \mathbb{Z}[\mathbb{R}] \to \mathbb{R} \to 0$$
Scholze refers to the spectral sequence arising from this complex to later talk about sheaf cohomology, but I am not sure what he means. Maybe he uses the filtration induced by truncation?
A similar thing is referenced in his notes (see Corollary 4.8), where he has a resolution and in that case he mentions this is obtained by applying RHom, but I am not sure how you get a spectral sequence then either.