THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY

David Gepner; Jeremiah Heller

doi:10.1017/S1474748021000372

THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY

David Gepner, Jeremiah Heller

Mathematics

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

Abstract

We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed-point functors and the motivic Adams isomorphism.

Original language	English (US)
Pages (from-to)	1181-1250
Number of pages	70
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	22
Issue number	3
DOIs	https://doi.org/10.1017/S1474748021000372
State	Published - May 10 2023

Keywords

Adams isomorphism
equivariant homotopy theory
motivic homotopy theory
tom Dieck splitting

ASJC Scopus subject areas

Mathematics(all)

Online availability

10.1017/S1474748021000372

Library availability

Discover UIUC Full Text

Cite this

@article{a911a9826343499d9b301355004edd45,

title = "THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY",

abstract = "We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed-point functors and the motivic Adams isomorphism.",

keywords = "Adams isomorphism, equivariant homotopy theory, motivic homotopy theory, tom Dieck splitting",

author = "David Gepner and Jeremiah Heller",

note = "Funding Information: The first author was supported by DFG award GE 2504/1-1 and NSF award DMS-1714273. The second author was supported by DFG award HE6740/1-1 and NSF award DMS-1710966. Publisher Copyright: {\textcopyright} The Author(s), 2021. Published by Cambridge University Press.",

year = "2023",

month = may,

day = "10",

doi = "10.1017/S1474748021000372",

language = "English (US)",

volume = "22",

pages = "1181--1250",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

publisher = "Cambridge University Press",

number = "3",

}

TY - JOUR

T1 - THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY

AU - Gepner, David

AU - Heller, Jeremiah

N1 - Funding Information: The first author was supported by DFG award GE 2504/1-1 and NSF award DMS-1714273. The second author was supported by DFG award HE6740/1-1 and NSF award DMS-1710966. Publisher Copyright: © The Author(s), 2021. Published by Cambridge University Press.

PY - 2023/5/10

Y1 - 2023/5/10

N2 - We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed-point functors and the motivic Adams isomorphism.

AB - We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed-point functors and the motivic Adams isomorphism.

KW - Adams isomorphism

KW - equivariant homotopy theory

KW - motivic homotopy theory

KW - tom Dieck splitting

UR - http://www.scopus.com/inward/record.url?scp=85119412476&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85119412476&partnerID=8YFLogxK

U2 - 10.1017/S1474748021000372

DO - 10.1017/S1474748021000372

M3 - Article

AN - SCOPUS:85119412476

SN - 1474-7480

VL - 22

SP - 1181

EP - 1250

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 3

ER -

THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this