On the slice spectral sequence for quotients of norms of Real bordism

Abstract In this paper, we investigate equivariant quotients of the Real bordism spectrum's multiplicative norm by permutation summands. These quotients are of interest because of their close relationship with higher real ‐theories. We introduce new techniques for computing the equivariant homotopy groups of such quotients. As a new example, we examine the theories . These spectra serve as natural equivariant generalizations of connective integral Morava ‐theories. We provide a complete computation of the ‐localized slice spectral sequence of , where is the real sign representation of . To achieve this computation, we establish a correspondence between this localized slice spectral sequence and the ‐based Adams spectral sequence in the category of ‐modules. Furthermore, we provide a full computation of the ‐localized slice spectral sequence of the height‐4 theory . The ‐slice spectral sequence can be entirely recovered from this computation.