On equivariant topological modular forms

TL;DR

This paper develops a general construction of equivariant elliptic cohomology inspired by Lurie's ideas, extending to positive characteristic and computing fixed points for circle groups and tori.

Contribution

It introduces a new, characteristic-independent approach to equivariant elliptic cohomology and constructs equivariant spectra of topological modular forms.

Findings

Computed fixed points of spectra for circle group

Extended equivariant elliptic cohomology beyond characteristic zero

Constructed equivariant spectra of topological modular forms

Abstract

Following ideas of Lurie, we give in this article a general construction of equivariant elliptic cohomology without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain in particular equivariant spectra of topological modular forms. We compute the fixed points of these spectra for the circle group and more generally for tori.