Motivic modular forms from equivariant stable homotopy theory

2017/04/14 by Ricka, Nicolas
#14F42 #55N91 #55P42 #55S10 #55T15 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.04547

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.

Related

• C-motivic modular forms
• The homotopy of C-motivic modular forms
• The cohomology of ℝ-motivic A(2)
• The cohomology of motivic A(2)
• A cellular absolute motivic ring spectrum representing Hermitian K-theory