For Complex Orientations Preserving Power Operations, p-typicality is Atypical
| DOI: | 10.48550/arxiv.0910.3187 |
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| Přístupová URL adresa: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::79f3b1c8d366b460cdc3d84d1f656d3f |
| Rights: | OPEN |
| Přírůstkové číslo: | edsair.doi.dedup.....79f3b1c8d366b460cdc3d84d1f656d3f |
| Autor: | Niles Johnson, Justin Noel |
| Rok vydání: | 2009 |
| Předmět: |
Pure mathematics
Ring (mathematics) Brown Peterson spectrum Conjecture Spectrum (functional analysis) Formal group H infinity orientation Complex cobordism Factorization 55N20 (Primary) 55S25 55R77 (Secondary) FOS: Mathematics Algebraic Topology (math.AT) Canonical map Power operations Mathematics - Algebraic Topology Geometry and Topology Commutative property Mathematics |
| DOI: | 10.48550/arxiv.0910.3187 |
| Popis: | 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. Minor revisions, results extended up to the prime 13. Accepted for publication. 22 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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