Hodge theory for elliptic curves and the Hopf element ν$\nu$

Abstract

AbstractWe show that the vector bundle on the moduli stack of elliptic curves associated to the 2‐cell complex is isomorphic to the de Rham cohomology sheaf of the universal elliptic curve . We use this to calculate the homotopy groups of the ‐quotient of by , called the spectrum of ‘topological quasimodular forms’, by relating its Adams–Novikov spectral sequence to the cohomology of the moduli stack of cubic curves with a chosen splitting of the Hodge–de Rham filtration.