Two-column degeneration of a Künneth spectral sequence ($E_2=E_{\infty }$)

If only the columns $p=-1,0$ are nonzero, a cohomological differential of bidegree $(r,1-r)$ has no possible nonzero source-target pair for $r\ge 2$. Projective boundaries in a complex of projectives give this condition because every cohomology module has projective dimension at most one.