Motivic modular forms from equivariant stable homotopy theory

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 C 2 -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.

The motivic Mahowald invariant

“…Remark 3.13. Analogously, one can define an exotic motivic analog of the motivic modular forms spectrum mmf [32] by defining wtmf to be the Cτ -module corresponding to the BP * BP -comodule…”