On the dual of a P-algebra and its comodules, with applications to comparison of some Bousfield classes

Baker, A. (2021) On the dual of a P-algebra and its comodules, with applications to comparison of some Bousfield classes. Technical Report. arXiv. (Submitted)

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Publisher's URL: https://arxiv.org/abs/2103.01253

Abstract

In his seminal work on localisation of spectra, Ravenel initiated the study of Bousfield classes of spectra related to the chromatic perspective. In particular he showed that there were infinitely many distinct Bousfield classes between ⟨MU⟩ and ⟨S⟩. The main topological goal of this paper is investigate how these Bousfield classes are related to that of another classical Thom spectrum MSp, and in particular how ⟨MSp⟩ is related to ⟨MU⟩. We follow the approach of Ravenel, but adapt it using the theory of P-algebras to give vanishing results for cohomology. Our work involves dualising and considering comodules over duals of P-algebras; these ideas are then applied to the mod 2 Steenrod algebra and certain subHopf algebras.

Item Type:Research Reports or Papers (Technical Report)
Status:Submitted
Glasgow Author(s) Enlighten ID:Baker, Dr Andrew
Authors: Baker, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Publisher:arXiv
Copyright Holders:Copyright © 2021 The Author
Publisher Policy:Reproduced under a Creative Commons License

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