Constructing the determinant sphere using a Tate twist

Tobias Barthel, Agnès Beaudry, Paul G. Goerss*, Vesna Stojanoska

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Following an idea of Hopkins, we construct a model of the determinant sphere S⟨ det ⟩ in the category of K(n)-local spectra. To do this, we build a spectrum which we call the Tate sphere S(1). This is a p-complete sphere with a natural continuous action of Zp×. The Tate sphere inherits an action of Gn via the determinant and smashing Morava E-theory with S(1) has the effect of twisting the action of Gn. A large part of this paper consists of analyzing continuous Gn-actions and their homotopy fixed points in the setup of Devinatz and Hopkins.

Original languageEnglish (US)
Pages (from-to)255-274
Number of pages20
JournalMathematische Zeitschrift
Volume301
Issue number1
DOIs
StatePublished - May 2022

ASJC Scopus subject areas

  • Mathematics(all)

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