Invariant prime ideals in equivariant Lazard rings

TL;DR

This paper computes the invariant prime ideals of the $A$-equivariant Lazard ring, linking it to the moduli stack of $A$-equivariant formal groups and the Balmer spectrum of compact $A$-spectra.

Contribution

It provides a detailed description of the spectrum of invariant prime ideals in the equivariant Lazard ring and establishes a homeomorphism with the Balmer spectrum.

Findings

Spectrum of invariant prime ideals computed

Homeomorphism with Balmer spectrum established

Connection with equivariant complex bordism homology made

Abstract

Let $A$ be an abelian compact Lie group. In this paper 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.