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

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