The Hecke algebra action on Morava E-theory of height 2
Abstract
Given a one-dimensional formal group of height 2, let E be the Morava E-theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an algebra of Hecke operators acting on E-cohomology. This leads to a vanishing result for Rezk's logarithmic cohomology operation on the units of E. It identifies a family of elements in the kernel with meromorphic modular forms whose Serre derivative is zero. Our calculation finds a connection to logarithms of modular units. In particular, we work out an action of Hecke operators on certain "logarithmic" q-series, in the sense of Knopp and Mason, that agrees with our vanishing result and extends the classical Hecke action on modular forms.
Keywords
Cite
@article{arxiv.1505.06377,
title = {The Hecke algebra action on Morava E-theory of height 2},
author = {Yifei Zhu},
journal= {arXiv preprint arXiv:1505.06377},
year = {2020}
}