For Complex Orientations Preserving Power Operations, p-typicality is Atypical

Niles Johnson; Justin Noel

doi:10.1016/j.topol.2010.06.007

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arXiv · 0910.3187

For Complex Orientations Preserving Power Operations, p-typicality is Atypical

Niles Johnson·Justin Noel

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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.

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BibTeX RIS

Niles Johnson, Justin Noel. 2009-10-16. For Complex Orientations Preserving Power Operations, p-typicality is Atypical. https://doi.org/10.1016/j.topol.2010.06.007

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