We investigate -cohomology of some commutative cooperation algebras associated with certain periodic cohomology theories. For KU and , the Adams summand at a prime , and for KO we show that -cohomology vanishes above degree 1. As these cohomology groups are the obstruction groups in the obstruction theory developed by Alan Robinson we deduce that these spectra admit unique structures. As a consequence we obtain an structure for the connective Adams summand. For the Johnson--Wilson spectrum with we establish the existence of a unique structure for its -adic completion.
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Andrew Baker, Birgit Richter, On the -cohomology of rings of numerical polynomials. Comment. Math. Helv. 80 (2005), no. 4, pp. 691–723DOI 10.4171/CMH/31