At the prime 2, the connective higher real K-theories eo_h are shown to be fp spectra of type h, which implies a divisibility constraint on Euler characteristics and a new obstruction to generalized Moore spectra.
Transchromatic phenomena in the equivariant slice spectral sequence
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In this paper, we prove a transchromatic phenomenon for Hill--Hopkins--Ravenel and Lubin--Tate theories. This establishes a direct relationship between the equivariant slice spectral sequences of height-$h$ and height-$(h/2)$ theories. As applications of this transchromatic phenomenon, we prove periodicity and vanishing line results for these theories.
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On higher real $K$-theories and finite spectra
At the prime 2, the connective higher real K-theories eo_h are shown to be fp spectra of type h, which implies a divisibility constraint on Euler characteristics and a new obstruction to generalized Moore spectra.