The slice spectral sequence for the C₄ analog of real K-theory

We describe the slice spectral sequence of a 32-periodic C4-spectrum K[2] related to the C4 norm MU((C4)) = NC4 C2MUR of the real cobordism spectrum MUR. We will give it as a spectral sequence of Mackey functors converging to the graded Mackey functor p∗K[2], complete with differentials and exotic extensions in the Mackey functor structure. The slice spectral sequence for the 8-periodic real K-theory spectrum KR was frst analyzed by Dugger. The C8 analog of K[2] is 256-periodic and detects the Kervaire invariant classes ffj. A partial analysis of its slice spectral sequence led to the solution to the Kervaire invariant problem, namely the theorem that ffj does not exist for j = 7.