For Complex Orientations Preserving Power Operations, p-typicality is Atypical
Abstract
We show, for primes p less than or equal to 13, that a number of well-known MU_(p)-rings do not admit the structure of commutative MU_(p)-algebras. These spectra have complex orientations that factor through the Brown-Peterson spectrum and correspond to p-typical formal group laws. We provide computations showing that such a factorization is incompatible with the power operations on complex cobordism. This implies, for example, that if E is a Landweber exact MU_(p)-ring whose associated formal group law is p-typical of positive height, then the canonical map MU_(p) --> E is not a map of H_\infty ring spectra. It immediately follows that the standard p-typical orientations on BP, E(n), and E_n do not rigidify to maps of E_\infty ring spectra. We conjecture that similar results hold for all primes.
Keywords
Cite
@article{arxiv.0910.3187,
title = {For Complex Orientations Preserving Power Operations, p-typicality is Atypical},
author = {Niles Johnson and Justin Noel},
journal= {arXiv preprint arXiv:0910.3187},
year = {2010}
}
Comments
Minor revisions, results extended up to the prime 13. Accepted for publication. 22 pages