Motivated by the study of chromatic phenomena in the classical and motivic Adams spectral sequences, we set up a machinery to build a spectrum (over \(\mathrm{Spec}(\mathbb{R})\) or \(\mathrm{Spec}(\mathbb{C}))\) of motivic modular forms (mmf), that is, a ring spectrum whose cohomology is A//A(2). This answers a question raised by Dan Isaksen. The approach we suggest makes a detour by C_2-equivariant stable homotopy theory, and uses the proximity between the equivariant and motivic Steenrod algebras, a relationship which is not shared by the classical Steenrod algebra. If time permits, we will talk about uniqueness of such spectra, and the chromatic consequences of mmf.

Pretalk at 3:00 in Hylan 1106B.