Multiplicative Structures on Brown–Peterson Spectra at Odd Primes

Abstract

We show that the odd-primary Brown-Peterson spectrum does not admit the structure of an E₂₍ₚ^₂ ₊₂₎ ring spectrum and that there can be no map MU → BP of E₂ₚ₊₃ ring spectra for odd primes p. This extends results of Lawson at the prime 2.