Motivic modular forms from equivariant stable homotopy theory

TL;DR

This paper constructs a cellular motivic spectrum of motivic modular forms over real and complex numbers, confirming a conjecture and introducing a new machinery linking equivariant and motivic spectra.

Contribution

It introduces a novel construction of motivic modular forms spectra from equivariant spectra, solving a conjecture and developing a potentially widely useful machinery.

Findings

Successfully constructed the motivic modular forms spectrum over $ $ and $ C$

Produced a $ G$-equivariant version of the spectrum

Developed a machinery to derive motivic spectra from equivariant spectra

Abstract

In this paper, we produce a cellular motivic spectrum of motivic modular forms over $\R$ and $\C$, answering positively to a conjecture of Dan Isaksen. This spectrum is constructed to have the appropriate cohomology, as a module over the relevant motivic Steenrod algebra. We first produce a $\G$-equivariant version of this spectrum, and then use a machinery to construct a motivic spectrum from an equivariant one. We believe that this machinery will be of independent interest.