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arXiv · 2504.07874

Power Operations on $K(n-1)$-Localized Morava $E$-theory at Height $n$

Yifan Wu
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Abstract

We calculate the $K(n-1)$-localized $E_n$ theory for symmetric groups, and deduce a modular interpretation of the total power operation $ψ^p_F$ on $F=L_{K(n-1)}E_n$ in terms of augmented deformations of formal groups and their subgroups. We compute the Dyer-Lashof algebra structure over $K(n-1)$-local $E_n$-algebra. Then we specify our calculation to the $n=2$ case. We calculate an explicit formula for $ψ^p_F$ using the formula of $ψ^p_E$, and explain connections between these computations and elliptic curves, modular forms and $p$-divisible groups.

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Yifan Wu. 2025-04-10. Power Operations on $K(n-1)$-Localized Morava $E$-theory at Height $n$. https://arxiv.org/abs/2504.07874

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