Brown-Peterson Spectrum

The Brown-Peterson spectrum at a prime is the -typical summand of -local complex cobordism. In its usual coefficient convention,

where . The truncated spectrum has coefficient ring . Morava K-theory isolates a chromatic height, whereas Smith-Toda complexes realize finite quotients killing and an initial string of these generators. A specification of homology as a comodule includes its coaction as well as its underlying graded module.