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arXiv · 1505.06377

The Hecke algebra action on Morava E-theory of height 2

Yifei Zhu
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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.

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Yifei Zhu. 2015-05-23. The Hecke algebra action on Morava E-theory of height 2. https://doi.org/10.1090/tran%2F8032

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