Ravenel's algebraic extensions of the sphere spectrum do not exist
Algebraic Topology
2016-07-06 v2 Algebraic Geometry
Number Theory
Abstract
In this paper we prove a topological nonrealizability theorem: certain classes of graded -modules are shown to never occur as the -homology of a spectrum. Many of these -modules admit the structure of -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.
Keywords
Cite
@article{arxiv.1511.04827,
title = {Ravenel's algebraic extensions of the sphere spectrum do not exist},
author = {A. Salch},
journal= {arXiv preprint arXiv:1511.04827},
year = {2016}
}