Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Devalapurkar, Sanath K., Levy, Ishan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7223874507