Chromatic Cyclotomic Extensions
Algebraic Topology
2024-12-25 v2
Abstract
We construct Galois extensions of the T(n)-local sphere, lifting all finite abelian Galois extensions of the K(n)-local sphere. This is achieved by realizing them as higher semiadditive analogues of cyclotomic extensions. Combining this with a general form of Kummer theory, we lift certain elements from the K(n)-local Picard group to the T(n)-local Picard group.
Cite
@article{arxiv.2103.02471,
title = {Chromatic Cyclotomic Extensions},
author = {Shachar Carmeli and Tomer M. Schlank and Lior Yanovski},
journal= {arXiv preprint arXiv:2103.02471},
year = {2024}
}
Comments
53 pages. Edited in response to comments of the referee. Fixed typos, some arguments expanded and made more precise, added details in section 5.2. Accepted to GnT