Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2

Details Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2 Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2

2012-03-08

arxiv.org/abs/1203.1696v1

Mathematics

Algebraic Topology

38 pages

Scientific paper

Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E_infinity-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map forgetting this level structure induces an E_infinity-ring map from the spectrum of topological modular forms to this truncated Brown-Peterson spectrum, and that this orientation fits into a diagram of E_infinity-ring spectra lifting a classical diagram of modules over the mod-2 Steenrod algebra. In an appendix we document how to organize Morava's forms of K-theory into a sheaf of E_infinity-ring spectra.

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