PreprintCC BY-NC-ND 4.0arXiv
Ramification in En-algebras
Abstract
We study En-algebras with ramification in their π0 and in particular show that the existence of ramification places strong limitations on their chromatic behavior. In particular, we show that π0 of nonzero K(1)-local E4-KU-algebras cannot have a map from the ring of integers in a ramified extension of Qp, and we show that a p-complete E2-ring with a map from a perfectoid ring into its π0 is an associative Zp-algebra.
Related
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BibTeX
@misc{devalapurkar2026ramification,
title = {{Ramification in $\mathbfE_n$-algebras}},
author = {Sanath K. Devalapurkar and Ishan Levy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33754},
eprint = {2610.33754},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33754},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Ramification in E_n-algebras
AU - Sanath K. Devalapurkar
AU - Ishan Levy
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33754
UR - https://arxiv.org/abs/2610.33754
AB - We study 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 E_4-KU-algebras cannot have a map from the ring of integers in a ramified extension of Q_p, and we show that a p-complete E_2-ring with a map from a perfectoid ring into its π_0 is an associative Z_p-algebra.
ER -