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arXiv · 2610.33754

Ramification in $\mathbf{E}_{n}$-algebras

Sanath K. Devalapurkar·Ishan Levy
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Abstract

We study $\mathbf{E}_n$-algebras with ramification in their $π_0$ and in particular show that the existence of ramification places strong limitations on their chromatic behavior. In particular, we show that $π_0$ of nonzero $K(1)$-local $\mathbf{E}_4$-$\mathrm{KU}$-algebras cannot have a map from the ring of integers in a ramified extension of $\mathbf{Q}_p$, and we show that a $p$-complete $\mathbf{E}_2$-ring with a map from a perfectoid ring into its $π_0$ is an associative $\mathbf{Z}_p$-algebra.

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Sanath K. Devalapurkar, Ishan Levy. 2026-10-24. Ramification in $\mathbf{E}_{n}$-algebras. https://arxiv.org/abs/2610.33754

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