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arXiv · 1511.04827

Ravenel's algebraic extensions of the sphere spectrum do not exist

A. Salch
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Abstract

In this paper we prove a topological nonrealizability theorem: certain classes of graded $BP_*$-modules are shown to never occur as the $BP$-homology of a spectrum. Many of these $BP_*$-modules admit the structure of $BP_*BP$-comodules, meaning that their topological nonrealizability does not follow from earlier results like Landweber's filtration theorem. As a consequence we solve Ravenel's 1983 problem on the existence of "algebraic extensions of the sphere spectrum": algebraic extensions of the sphere spectrum do not exist, except in trivial cases.

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A. Salch. 2015-11-16. Ravenel's algebraic extensions of the sphere spectrum do not exist. https://arxiv.org/abs/1511.04827

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