Invariant prime ideals in equivariant Lazard rings

Hausmann, Markus; Meier, Lennart

doi:10.2140/gt.2025.29.3813

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Invariant prime ideals in equivariant Lazard rings

Markus Hausmann and Lennart Meier

Geometry & Topology 29 (2025) 3813–3871

DOI: 10.2140/gt.2025.29.3813

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.

Keywords

equivariant formal group, Balmer spectrum, equivariant Lazard ring

Mathematical Subject Classification

Primary: 14L05, 55N22, 57R85

Secondary: 55P91

References

Publication

Received: 5 January 2024

Revised: 4 November 2024

Accepted: 25 January 2025

Published: 10 October 2025

Proposed: Mark Behrens

Seconded: Haynes R Miller, Marc Levine

Authors

Markus Hausmann
Mathematisches Institut Universität Bonn Bonn Germany

Lennart Meier
Mathematical Institut Universiteit Utrecht Utrecht Netherlands

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Volume 29, issue 7 (2025)