Abstract: In Cohen’s famous calculation of the mod p cohomology of configuration spaces, the key ingredient was a complete description of the Cartan–Leray spectral sequence for the configuration space of k = p points. In this talk, I will discuss this, aiming at giving a complete description of this spectral sequence for arbitrary k. This work not only provides a geometric way to prove the Arone–Mahowald theorem and Kjaer’s theorem, but also gives the potential to determine the ring structure of cohomology of unordered configuration spaces.