Invariant prime ideals in equivariant Lazard rings

Markus Hausmann; Lennart Meier

doi:10.2140/gt.2025.29.3813

Invariant prime ideals in equivariant Lazard rings

Markus Hausmann, Lennart Meier

Sub Fundamental Mathematics

University of Bonn

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

Abstract

Let A be an abelian compact Lie group. We compute the spectrum of invariant prime ideals of the A-equivariant Lazard ring, or equivalently the spectrum of points of the moduli stack of A-equivariant formal groups. We further show that this spectrum is homeomorphic to the Balmer spectrum of compact A-spectra, with the comparison map induced by equivariant complex bordism homology.

Original language	English
Pages (from-to)	3813-3871
Number of pages	59
Journal	Geometry and Topology
Volume	29
Issue number	7
DOIs	https://doi.org/10.2140/gt.2025.29.3813
Publication status	Published - 10 Oct 2025

Bibliographical note

Publisher Copyright:
© 2025 The Authors, under license to MSP (Mathematical Sciences Publishers).

Keywords

Balmer spectrum
equivariant formal group
equivariant Lazard ring

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10.2140/gt.2025.29.3813Licence: CC BY

Invariant prime ideals in equivariant Lazard ringsFinal published version, 863 KBLicence: CC BY

Cite this

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title = "Invariant prime ideals in equivariant Lazard rings",

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T1 - Invariant prime ideals in equivariant Lazard rings

AU - Hausmann, Markus

AU - Meier, Lennart

PY - 2025/10/10

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N2 - Let A be an abelian compact Lie group. We compute the spectrum of invariant prime ideals of the A-equivariant Lazard ring, or equivalently the spectrum of points of the moduli stack of A-equivariant formal groups. We further show that this spectrum is homeomorphic to the Balmer spectrum of compact A-spectra, with the comparison map induced by equivariant complex bordism homology.

AB - Let A be an abelian compact Lie group. We compute the spectrum of invariant prime ideals of the A-equivariant Lazard ring, or equivalently the spectrum of points of the moduli stack of A-equivariant formal groups. We further show that this spectrum is homeomorphic to the Balmer spectrum of compact A-spectra, with the comparison map induced by equivariant complex bordism homology.

KW - Balmer spectrum

KW - equivariant formal group

KW - equivariant Lazard ring

UR - https://www.scopus.com/pages/publications/105019980785

U2 - 10.2140/gt.2025.29.3813

DO - 10.2140/gt.2025.29.3813

M3 - Article

AN - SCOPUS:105019980785

SN - 1465-3060

VL - 29

SP - 3813

EP - 3871

JO - Geometry and Topology

JF - Geometry and Topology

IS - 7

ER -

Invariant prime ideals in equivariant Lazard rings

Abstract

Bibliographical note

Keywords

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Invariant prime ideals in equivariant Lazard rings

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