Constructing the determinant sphere using a Tate twist

Tobias Barthel; Agnès Beaudry; Paul G. Goerss; Vesna Stojanoska

doi:10.1007/s00209-021-02864-x

Constructing the determinant sphere using a Tate twist

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

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 G_n via the determinant and smashing Morava E-theory with S(1) has the effect of twisting the action of G_n. A large part of this paper consists of analyzing continuous G_n-actions and their homotopy fixed points in the setup of Devinatz and Hopkins.

Original language	English (US)
Pages (from-to)	255-274
Number of pages	20
Journal	Mathematische Zeitschrift
Volume	301
Issue number	1
DOIs	https://doi.org/10.1007/s00209-021-02864-x
State	Published - May 2022

Funding

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1812122 and Grant No. DMS-1725563. Barthel was partially supported by the DNRF92 and the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 751794. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the program Homotopy Harnessing Higher Structures when work on this paper was undertaken. This work was supported by EPSRC Grant Number EP/R014604/1.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00209-021-02864-x

Cite this

@article{bea4dfe0e7b743c199df65ec2495949b,

title = "Constructing the determinant sphere using a Tate twist",

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.",

author = "Tobias Barthel and Agn{\`e}s Beaudry and Goerss, {Paul G.} and Vesna Stojanoska",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

month = may,

doi = "10.1007/s00209-021-02864-x",

language = "English (US)",

volume = "301",

pages = "255--274",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Constructing the determinant sphere using a Tate twist

AU - Barthel, Tobias

AU - Beaudry, Agnès

AU - Goerss, Paul G.

AU - Stojanoska, Vesna

PY - 2022/5

Y1 - 2022/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85120655544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85120655544&partnerID=8YFLogxK

U2 - 10.1007/s00209-021-02864-x

DO - 10.1007/s00209-021-02864-x

M3 - Article

AN - SCOPUS:85120655544

SN - 0025-5874

VL - 301

SP - 255

EP - 274

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1

ER -

Constructing the determinant sphere using a Tate twist

Abstract

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this